Competitive exams have at least one question where you have to find the square root of a number in seconds. With the help of this shortcut method, you can find square root of a number within seconds. This method is applicable only for perfect squares. The Square root questions asked in competitive exams/bank exams & entrance exams are usually perfect squares. Refer How to check if a number is a perfect square? to find out if a given number is a perfect square.
Math Trick
Sum of Consecutive Numbers Shortcut
Finding the sum of consecutive numbers is a common question asked in competitive exams. You can now find the sum of consecutive numbers starting with 1, the sum of consecutive odd numbers, and the sum of consecutive even numbers in seconds.
What are consecutive numbers?
Numbers that follow each other in order are Consecutive numbers. Here the difference between every two numbers is 1. The consecutive numbers can be represented as n,n+1,n+2.
Examples of consecutive numbers:
(1)1,2,3,4,5,6,7,8
(2)6,7,8,9,10,11
Sum of consecutive numbers starting from 1 shortcut
Now that we know what consecutive numbers are. We shall see a shortcut to find the sum of consecutive numbers starting from 1.
It can be represented as sum of n consecutive numbers = n+(n+1)+(n+2)
Sum of consecutive numbers starting from 1 shortcut steps
Step 1:Count the total number of integers from 1 to the last consecutive number given.
Step 2:Multiply the result in step 1 by 1 more than the number.
Step 3:Divide the result of step 2 by 2.
We shall see some examples to understand better
Example 1:Find the sum of all consecutive numbers from 1 to 9.
Step 1: Counting the number of integers from 1 to 9. We find that there are 9 integers.
Step2: Multiplying the number of integers(9) by 1 more than the number that is 10.
We get, 9 X 10=90
Step3: Dividing the result obtained in step2 by 2
we get, 90/2=45
Ans Hence, the sum of consecutive numbers from 1 to 9=45
Example 2:Find the sum of all consecutive numbers from 1 to 99.
Step 1: Counting the number of integers from 1 to 99. We find that there are 99 integers.
Step2: Multiplying the number of integers(99) by 1 more than the number that is 100.
We get, 99 X 100=9900
Step3: Dividing the result obtained in step2 by 2
we get, 9900/2=4950
Ans Hence, sum of consecutive numbers from 1 to 99=4,950
Odd Consecutive numbers
Odd numbers that follow each other are consecutive odd numbers. Here the difference between every two odd numbers is 2.
It can be represented as Sum of n numbers = n+(n+2)+(n+4)+(n+6) where n is an odd number..
We shall see how to add odd consecutive numbers.
Sum of consecutive odd numbers starting from 1 steps
Step 1: Count the total number of odd integers from 1 to the last consecutive number given.
Step 2: Square the result obtained in step 1.
Example 1:Find the sum of all consecutive odd numbers from 1 to 10.
Step 1: Counting the number of integers from 1 to 9. We find that there are 5 integers.
Step 2: Squaring the result obtained in step 1.
We get, 52=25
Ans hence, Sum of odd numbers from 1 to 9 is 25
Example 2:Find the sum of all consecutive odd numbers from 1 to 100.
Step 1: Counting the number of integers from 1 to 100. We find that there are 50 integers.
Step 2: Squaring the result obtained in step 1.
We get, 502=2500
Ans 2500
Even Consecutive numbers
Even numbers that follow each other are consecutive even numbers. Here the difference between every two even numbers is 2.
It can be represented as Sum of n numbers = n+(n+2)+(n+4)+(n+6)where n is an even number.
We shall see how to add even consecutive numbers.
Sum of consecutive even numbers starting from 2 steps
Step 1: Count the total number of odd integers from 1 to the last consecutive number given.
Step 2: Multiply the result in step 1 by 1 more than the number.
Example 1:Find the sum of all consecutive even numbers from 1 to 10.
Step 1: Counting the number of integers from 1 to 10. We find that there are 5 integers.
Step 2: Multiplying the number of integers(5) by 1 more than the number that is 6.
We get, 5 X 6=30
Ans 30
Example 2:Find the sum of all consecutive even numbers from 1 to 100.
Step 1: Counting the number of integers from 1 to 100. We find that there are 50 integers.
Step 2: Multiplying the number of integers(50) by 1 more than the number that is 51.
We get, 50 X 51=2550
Ans 2550.
2 digit Multiplication Trick with Same Tens digit
You must be wondering we have learned so many multiplication tricks for 2 digit numbers, so how is this going to be helpful. Well, Knowing new tricks and where the trick can be applied to get the answer quickly can make all the difference. 2 digit multiplication trick or double digit multiplication trick whose tens digit is the same is one of those tricks that we will explore today.
Shortcut to find Square Root
Shortcut to find Square Root of any Number
In every competitive exam, there is at least one instance where you will have to find the square root of a number quickly. With the help of this shortcut on how to find the square root of a number, you will be able to find out the square root of any number within seconds. This method is applicable only for perfect squares. Square root questions asked in competitive exams/bank exams are usually perfect squares. Refer How to check if a number is a perfect square? to find out if a given number is a perfect square.
Steps to Find the Square Root of a Number
Step 1: First of all group the number in pairs of 2 starting from the right.
Step 2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the square.
Step 3: To get the unit’s place digit of the square root
Remember the following
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If the number ends in
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Unit’s place digit of the square root
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1
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1 or 9(10-1)
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4
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2 or 8(10-2)
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9
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3 or 7(10-3)
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6
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4or 6(10-4)
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5
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5
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0
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0
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Let’s see the logic behind this method to find square root for a better understanding
We know,
12=1
22=4
32=9
42=16
52=25
62=36
72=49
82=64
92=81
102=100
Now, observe the unit’s place digit of all the squares.
Do you find anything common?
We notice that,
Unit’s place digit of both 12and 92 is 1.
Unit’s place digit of both 22 and 82 is 4
And Unit’s place digit of both 32 and 72 is 9
Unit’s place digit of both 42 and 62 is 6.
Step 4: Multiply the ten’s place digit (found in step 1) with its consecutive number and compare the result obtained with the first pair of the original number from left.
Remember,
If the first pair of the original number > Result obtained on multiplication then select the greater number out of the two numbers as the unit’s place digit of the square root.
If the first pair of the original number < the result obtained on multiplication, then select the lesser number out of the two numbers as the unit’s place digit of the square root.
Let us consider an example to get a better understanding of the method
Shortcut to find the square root of a 3 Digit Number
Example 1: √784=?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
7 84
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (7) is 4 and √4=2
Therefore, ten’s place digit=2.
Step 3: To get the unit’s place digit,
We notice that the number ends with 4, So the unit’s place digit of the square root should be either 2 or 8(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(2) and its consecutive number(3) we get,
2 x 3=6
ten’s place digit of original number > Multiplication result
7>6
So we need to select the greater number (8) as the unit’s place digit of the square root.
Unit’s place digit =8
Ans:√784=28
Shortcut to find the square root of any 4 digit number
Example 2: √3721?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
37 21
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (37)is 36 and√36=6
Therefore ten’s place digit=6
Step 3: To get the unit’s place digit,
We notice that the number ends with 1, So the unit’s place digit of the square root should be either 1 or 9(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(6) and its consecutive number(7) we get,
6 x 7=42
ten’s place digit of an original number<Multiplication result
37 < 42
So we need to select the lesser number (1) as the unit’s place digit of the square root.
Unit’s place digit =1
Ans:√3721=61
How to find square root shortcut
Example 3: √6889?
Step 1: We start by grouping the numbers in pairs of two from the right as follows
68 89
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (68)is 64 and√64=8
Therefore ten’s place digit=8
Step 3: To get the unit’s place digit,
We notice that the number ends with 9, So the unit’s place digit of the square root should be either 3 or 7(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(8) and its consecutive number(9) we get,
8 x 9 =72
ten’s place digit of an original number<Multiplication result
68 < 72
So we need to select the lesser number (3) as the unit’s place digit of the square root.
Unit’s place digit =3
Ans:√6889=83
Shortcut to find the square root of any 5 digit number
Example 4: √64516
Step 1: We start by grouping the numbers in pairs of two from the right as follows
645 16
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (645)is 625 and√625=25
Therefore ten’s place digit=25
Step 3: To get the unit’s place digit,
We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(25)and its consecutive number(26)we get,
25 x 26=650
ten’s place digit of an original number<Multiplication result
645< 650
So we need to select the lesser number (4) as the unit’s place digit of the square root.
Unit’s place digit =4
Ans:√64516=254
Shortcut to find the square root of any 6 digit number
Example 5: √126736
Step 1: We start by grouping the numbers in pairs of two from the right as follows. For a 6 digit number, this is how it should be paired.
1267 36
Step 2: To get the ten’s place digit,
We find that nearest square to the first group (1267)is 1225 and√1225=35
Therefore ten’s place digit=35
Step 3: To get the unit’s place digit,
We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer table).
Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(35)and its consecutive number(36)we get,
35 x 36=1260
ten’s place digit of original number>Multiplication result
1267>1260
So we need to select the greater number (6) as the unit’s place digit of the square root.
Unit’s place digit =6
Ans:√126736=356
Example 6: √207025
Step 1: We start by grouping the numbers in pairs of two from right as follows. For a 6 digit number, this is how it should be paired.
2070 25
Step 2: To get the tenth place digit,
We find that nearest square to the first group (2070) is 2025 and√2025=45. Therefore ten’s place digit=45
Step 3: To get the unit’s place digit,
We notice that the number ends with 5, So the unit’s place digit of the square root should be 5(Refer table).
Skip all the other steps for a number ending in 5
Unit’s place digit =5
Ans:√207025=455
Also, read Square root shortcut Non-perfect squares
Math Tricks for Bank Exams
You can get an edge over others in calculating at lightning speed. We can say “Speed Trills and Speed Scores”holds true for any competitive exam.You are racing against time to answer as many questions as possible in the least time. So here is a list of multiplication tricks, Tricks to find Cube roots and square roots, Squaring tricks, Cubing tricks, division tricks, verification tricks, percentage tricks, Subtraction tricks and Data Interpretation tricks that you can use to ace in bank exams. I have listed all the tricks that can be used as per scenario. However, if you learn even a handful of these tricks you will be ahead in the competition.
Let us now quickly jump into the tricks.
Math Tricks – Multiplication tricks
(1) Shortcut to multiply any 2digit by 2digit
This is a basic multiplication trick that you can use to multiply any 2 digit numbers from 10 to 99. It will take just 5 secs to multiply using this trick.
Learn the trick here Shortcut to multiply any 2digit by 2digit
(2)Shortcut to multiply any 2 digit number by 125
When you know that the given number is exactly divisible by 8, this is trick you should use to mentally multiply the number by 125. Learn the trick here Shortcut to multiply any 2 digit number by 125
(3)Shortcut to multiply any 2 digit number by 15
If the given number is easily divisible by 2, use this trick to multiply by 15 in less than 2 secs. Learn the trick here Shortcut to multiply any 2 digit number by 15
(4)Shortcut to multiply any 2 digit number by 11
Usually, a number will be given in the exam that is to be multiplied by 11 and the problem is not resolved here. It is just 1 part of the complex math problem given. In such problems, you can use this trick to save lot of time. It hardly takes 1 sec to get answer using this trick. Learn the trick here Shortcut to multiply any 2 digit number by 11
(5)Shortcut to multiply any 2 digit number by 111
If you have learnt the shortcut to multiply a 2 digit number by 11, then this trick is cakewalk for you. There is just a slight modification to the initial trick. Saving a second here and there gives you more time to solve more questions. Learn the trick here Shortcut to multiply any 2 digit number by 111
(6)Shortcut to multiply any number from 10-19 by 5
This trick works on the method of assuming convenient base closest to the number between 10 to 19. Assuming the correct base will make your calculation easier. Learn the trick here Shortcut to multiply any number from 10-19 by 5
(7)Shortcut to multiply any number from 20-29 by 5
If you learnt shortcut to multiply a number from 10 to 19 by 5, then this trick is simple. Only the number assumed as base will change. Learn the trick here Shortcut to multiply any number from 20-29 by 5
(8)Shortcut to multiply any number from 30-39 by 5
If you learnt shortcut to multiply a number from 20 to 29 by 5, then this trick is easy. Only the number assumed as base will change. Learn here Shortcut to multiply any number from 30-39 by 5
(9)Shortcut to multiply any number from 40-49 by 5
If you learnt shortcut to multiply a number from 30 to 39 by 5, then this trick is simple to apply to solve your math problems . Only the number assumed as base will change. Learn here Shortcut to multiply any number from 40-49 by 5
(10)Shortcut to multiply any number from 50-59 by 5
If you learnt shortcut to multiply a number from 40 to 49 by 5, then this trick is quite simple. Only the number assumed as base will change. Learn here Shortcut to multiply any number from 50-59 by 5
(11)Shortcut to multiply any number from 60-69 by 5
If you learnt shortcut to multiply a number from 50 to 59 by 5, then this trick is simple. Only the number assumed as base will change. Learn here Shortcut to multiply any number from 60-69 by 5
(12)Shortcut to multiply any number from 70-79 by 5
If you learnt shortcut to multiply a number from 60 to 69 by 5, then this trick is easy to learn. Only the number assumed as base will change. Learn here Shortcut to multiply any number from 70-79 by 5
(13)Shortcut to multiply any number from 80-89 by 5
If you learnt shortcut to multiply a number from 70 to 79 by 5, then this trick is simple. Only the number assumed as base will change. Learn here Shortcut to multiply any number from 80-89 by 5
(14)Multiply any 2 digit number with same ten’s place
When the ten’s place digit is same and the unit’s place digits add up to 10 then you can apply a shortcut trick to easily multiply any 2 digit numbers. Knowing where to apply this trick can make the difference. Learn here Multiply any 2 digit number with same ten’s place
(15)Shortcut to multiply 2 numbers whose difference is 2
This trick is especially effective to use when you know the square of the number in between the 2 numbers. Learn here Shortcut to multiply 2 numbers whose difference is 2
(16)How to multiply any two 3 digit number close to 100
This trick can be applied when the 2 given numbers are closer to 100. You can multiply mentally in seconds. How amazing is that? Learn here How to multiply any two 3 digit number close to 100
(17)Vedic math trick to multiply any 3 digit by 3 digit
This is a basic 3 digit multiplication trick. You can multiply any 3 digit number by a 3 digit number in seconds by using this trick rather than using the traditional multiplication method. This is very helpful trick for a person writing any of the competitive exams. Learn here Vedic math trick to multiply any 3 digit by 3 digit
(18)Shortcut to multiply any 3 digit number by 111
If you learnt the shortcut to multiply 2 digit number by 111. Then, there is just 1 more step added to it. And now use this trick to mentally multiply any 3 digit number by 111 in seconds. Learn here Shortcut to multiply any 3 digit number by 111
(19)Shortcut to multiply any number from 10-19 by 6
Learn here Shortcut to multiply any number from 10-19 by 6
Math Tricks – Cube roots and Square roots
(1)Shortcut find cube root of any 5 or 6 digit number
Finding cube root of any number has never been easier. You can now mentally find the cube root of any 4 digit number or 5 digit number or 6 digit number in seconds. Time saved is time earned. You can save a lot of time using this trick. Learn here Shortcut find cube root of any 5 or 6 digit number
(2)Shortcut to find square root of a number
You can ace in your bank exams if you know this trick.You can find the square root of any 4 digit number or 5 digit number or 6 digit number mentally in seconds. What more can you ask for. Check out some of the examples to perfect your skill. Learn here Shortcut to find square root of a number
Math Tricks – Squaring tricks
(1)Squaring a number ending with 5 in secs
Is it possible to square a number ending a number in less than a second. Yes, you can mentally find the square in less than 1 second if you know this trick. Learn here Squaring a number ending with 5 in secs
(2)Shortcut to square any number from 10-19
Square any number from 10 to 19 in seconds using this trick. Its a simple trick that you can use to mentally find the square. Learn here Shortcut to square any number from 10-19
(3)Shortcut to square any number from 20-29
This trick is similiar to the trick you learnt on “Square any number from 10 to 19”. Just a little variation and you can a square a number from 20-29 mentally in seconds. Learn here Shortcut to square any number from 20-29
(4)Shortcut to square any number from 30-79
This trick is similiar to the trick you learnt on “Square any number from 20 to 29”. Just a little variation and you can a square a number from 30-79 mentally in seconds. Learn here Shortcut to square any number from 30-79
(5)Shortcut to square any number from 90 to 99
This trick is similiar to the trick you learnt on “Square any number from 30 to 79”. Just a little variation and you can a square a number from 90-99 mentally in seconds. Learn here Shortcut to square any number from 90 to 99
(6)Shortcut to square any number from 100-120
This trick works by assuming a base method. Whenever you see a number close to 100, it must strike to you to use this trick to mentally find the square. Learn here Shortcut to square any number from 100-120
Division tricks
(1)Shortcut to divide any 2 digit number by 5
Here in this trick we will not be dividing the number. Instead we will be doubling the number.Wondering how we can arrive at the answer without dividing. Learn here Shortcut to divide any 2 digit number by 5
(2)Shortcut to divide any 2 digit number by 9
This trick is similiar to the trick used to multiply a 2 digit number by 11. There is just a slight variation to the trick. You can mentally divide any number by 9 in seconds. Learn here Shortcut to divide any 2 digit number by 9
Verification tricks
(1)How to verify if a number is a perfect cube
Learn how to verify if a number is perfect cube using Prime Factorization Method. It is the method to use to find out if a given number is a perfect cube or not if you want accurate results. Learn here How to verify if a number is a perfect cube
(2)How to verify if a number is a perfect square?
Using the prime factorization method we can find out if a given number is a perfect square or not. Learn here How to verify if a number is a perfect square?
(3) Vedic math trick to check multiplication
This is trick you can use to check if you have multiplied the numbers accurately. Learn here Vedic math trick to check multiplication
Percentage tricks
(1)Shortcut to find percentage of a number
This is one of the coolest trick which makes math fun. Understand the basic concept of percentages, practice and apply to problems in bank exams. You will love the way you arrive at the answer in seconds mentally. Learn here Shortcut to find percentage of a number
(2)How to convert fraction into percentage
If you already learnt the trick to find percentage of a number, this trick is an extension of the same.Go through the steps and you can mentally convert a fraction to percentage. Learn here How to convert fraction into percentage
Cubing tricks
(1)Shortcut to cube any number from 1 to 100
Remember the algebraic formula you learnt in school. We are going to manipulate the formula and use it to mentally find the cube of a number in seconds. Learn here Shortcut to cube any number from 1 to 100
Other Tricks
(1)Finding complement of a number
This is a simple trick using base method to find the complement of numbers from 1 to 1000. Knowing this trick will help you in subtracting any 2 numbers in seconds. Learn here Finding complement of a number
(2)Shortcut to subtract any 5 or 6 digit number in seconds
If you learnt the trick to find compliment of a number, then you can use that to subtract any 5 or 6 digit number in seconds mentally using this trick. Learn here Shortcut to subtract any 5 or 6 digit number in seconds
Data Interpretation Tricks
(1)Quantitative aptitude for clerical and bank po
In data Interpretation problems, finding average of a product sold in 3 years is a typical question in bank exam. To ace in this, use this trick to find the average number. Learn here Quantitative aptitude for clerical and bank po
(2)Data analysis questions and answers for bank po
Another typical data interpretation question asked in the Bank exams is “In which of the years was the percentage increase in production of company A was minimum from the previous year?”. Such questions can be easily solved using this amazing trick. Learn here Data analysis questions and answers for bank po
(3)Data interpretation trick for bar chart diagrams
Data analysis and interpretation problems are given to test how keenly you can observe things. You can solve a typical question such as “In which year the percentage increase or decrease in the production of company B to that of company A was maximum” in seconds using this trick. Learn here Data interpretation trick for bar chart diagrams
(4)Data interpretation trick to find percentage increase
You can solve another typical data interpretation question such as “percentage increase in the sale of a product in 1 year compared to the other year” in seconds. Learn here Data interpretation trick to find percentage increase
(5)Data interpretation trick for bank PO and clerical exams
You can solve another typical data interpretation question “In which year the percentage increase in the production of a company A to that of company B was minimum?” in seconds. Learn here Data interpretation trick for bank PO and clerical exams