How to verify if a number is perfect cube

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How to verify if a number is 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. Before going into the details of the Prime Factorization Method, it is helpful to know what Prime factors are.

Prime numbers are those numbers which are divisible only by 1 and the number itself. These numbers do not have any other divisible factors.

Prime numbers such as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29……. are also known as the prime factors.
Now, we shall see how Prime Factorization Method is done from the below steps.
Step 1: Find the prime factors of the given number.
Step 2:Group the factors in 3’s of equal factors.
Step 3:After grouping,
If you are not left with any separate single or double factor, then the given number is a perfect cube.
If you are left with any separate single or double factor, then the given number is not a perfect cube.
Let us consider some examples to understand the Prime Factorization Method better.

Examples

Example of a number which is a perfect cube.

Example1:Verify if 216 is a perfect cube.
Step1:We start by finding prime factors of 216.
prime factorization1
Prime factors of 216 are 2x2x2x3x3x3
Step 2: Grouping the factors into 3’s
          (2x2x2) x (3x3x3)
Step 3: After grouping, we notice that no factor is left.
Therefore we can say that 216 is definitely a perfect cube.

Example of a number which is not a perfect cube.

Example 2:Verify if 1024 is a perfect cube
Step1:We start by finding prime factors of 1024.
prime factorization
Prime factors of 1024 are 2x2x2x2x2x2x2x2x2x2
Step 2:Grouping the factors into 3’s
(2x2x2) x (2x2x2) x (2x2x2) x 2
Step 3: After grouping, we notice that factor 2 is left.
Therefore we can say that 1024 is not a perfect cube.

Shortcut to find cube of any number from 1 to 100

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Shortcut to find cube of any number from 1 to 100

Finding cube of a number above 20 in the usual way is difficult and time consuming. With this Shortcut to find cube of any number, you can easily calculate cube of a number within seconds.

Short cut to find cube of number steps

Step 1: Assume the ten’s place number of the given number as a and the unit’s place number as b.
Step 2: Now, we all know that (a+b)³=a³ + 3a²b + 3ab² + b³

We shall manipulate the same formula to calculate the cube of a number.

(i)Find b³ to get the last digit
 If you get two digit number then, add ten’s place digit to 3ab²
(ii) Find 3ab²
If you get two digit number then, keep the unit’s place digit and and
add ten’s place digit to 3a²b.

(iii) Find 3a²b
If you get two digit number then, keep the unit’s place digit and and
add ten’s place digit to a³.

(iv) Find a³
If you get two digit number then, just add the carried forward digit if any
and write the number.
Cube of any 2 digit number will be in the pattern of
a³ 3a²b  3ab² b³

Cube To make things easier it is good to memorize the cubes of numbers from
1 to 10
13=1
23=8
33=27
43=64
53=125
63=216
73=343
83=512
93=729

Examples

Lets use this method to calculate the cube of a number with help of an example to understand better

Example 1: 32³=?
Step 1: Assume a= 3 and b= 2
Step 2: Now substituting the values of a and b in the below pattern
a³ 3a²b  3ab² b³

(i) Finding b³  Now that is
b³=2³=8
We get the last digit as 8.

(ii) Finding 3ab²
3ab²=3(3)(2)²=36
From this we will keep the one’s place digit(6) and add the ten’s place digit(3) to 3a²b.

(iii)Finding 3a²b and adding ten’s place digit(3)
3a²b=3(3)²(2)=3(9)(2)=54 + 3= 57

From this we will keep the one’s place digit(7) and add ten’s place digit(5) to b in the next step.

(iv) Finding a³ and adding the ten’s place digit(5) from previous step
a³=3³=27+5=32
From this we get the number as 32

From all the above steps we get

Ans 32³=32768

Example 2: 47³=?
Step 1: Assume a= 4 and b= 7
Step 2: Now substituting the values of a and b in the below pattern
a³ 3a²b  3ab² b³

(i) Finding b³  Now that is
b³=73=343
We get the last digit as 3.

(ii) Finding 3ab²
3ab²=3(4)(7)²=12 x 49=588 (Tip: Use Shortcut to multiply any 2 digit by 2 digit)
Now add 34 that you got from step 1 to 588,we get  588+34=622
From this we will keep the one’s place digit(2) and add remaining digits(62) to 3ab².

(iii)Finding 3a²b and adding remaining digits of step 2(62)
3a²b=3(4)²(7)=16 x 21=336
336+ 62=398
From this we will keep the one’s place digit(8) and add remaining digits(39) to a³.

(iv) Finding a³ and adding the remaining digits from step 3
a³=4³=64
64 + 39=103

From all the above steps we get
47³=103823

With practice you will be able to find the cube of any two digit
number within seconds.

Try it  with other numbers and let us know if it was helpful to you!

If you have any other shortcut way of finding the cube of a number,
feel free to share it here.

Shortcut to Multiply 2 digit by 2 digit

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Shortcut to Multiply 2 digit by 2 digit

You can always use the method that we are used to in our school days to multiply any two numbers if you have sufficient time. However, bank exams is all about answering maximum number of questions accurately in limited time. How efficiently you manage time depends on how well you can apply the shortcut tricks that you learnt and practiced.

Multiply 2 digit by 2 digit shortcut method

Here is a shortcut to multiply any 2 digit number by a 2 digit number within seconds.

Let us see the steps to multiply a 2 digit number by a 2 digit number

Step 1:Multiply the ten’s place digit of the 1st number with ten’s place digit of the 2nd number to get the ten’s place digit of your answer.

Step 2:Leave a blank space in between.Now multiply the unit’s place digit of the 1st number with the unit’s place digit of the 2nd number to get the unit’s place digit of your answer.

Step 3:Find the product of the inside numbers and the product of the extremes and add both and insert the digit in the blank space.

Let us consider an example to understand better
Example 1: 41 x 31=?
Step 1:Multiply ten’s place digit of both the numbers as shown below

41 x 31=12 (i.e 4 x 3)
Step 2: Leave a blank space in between the ten’s place digit and unit place digit. 12_
Multiply unit’s place digit of both the numbers as shown below

41 x 31=1(i.e 1 x 1)
we get, 12_1
Step 3: Find the product of inside numbers(1 x 3=3)
Find the product of extremes (4 x 1=4)
41 x 31
Now adding the product of inside numbers and extremes
we get,
(1 x 3)+(4 x 1)=3+4=7
The middle digit is 7
Ans:    41 x 31=1271
Example 2: 46 x 36=?

Step 1: Multiply ten’s place digit of both the numbers as shown below

46 x 36=12(i.e 4 x 3)

Step 2: Leave a blank space in between the ten’s place digit and unit place digit as below.
12_
Multiply unit’s place digit of both the numbers as shown below to get the unit’s place digit which is 6

46 x 36=36 (i.e 6 x 6)
12_6
Here we are getting 2 digit number on multiplication, we will keep the unit’s place digit(6) and carry forward ten’s place digit(3) to step 3 as shown below
Step 3:Find the product of inside numbers(6 x 3=18)

Find the product of extremes (4 x 6=24)
46 x 36
Now adding the product of inside numbers and extremes
we get,18+24=42
Now we shall add the carry forward ten’s place digit(3) we got from step 2.
42+3=45
We shall keep unit’s place digit(5) and carry forward ten’s place digit(4) to step 1.
1256. Middle number is 5.
Step 4:Adding carry forward(4) from step 3 to step 1 answer, we get

12+4=16
Ans:    46 x 36=1656
Example 3: 32 x 34=?

Step 1: Multiply ten’s place digit of both the numbers as shown below

32 x 34=9(i.e 3 x 3)

Step 2: Leave a blank space in between the ten’s place digit and unit place digit as below.
9_
Multiply unit’s place digit of both the numbers as shown below to get the unit’s place digit which is 6

32 x 34=8 (i.e 4 x 2)
9_8
Step 3:Find the product of inside numbers(2 x 3=6)

Find the product of extremes (3 x 4=12)
32 x 34
Now adding the product of inside numbers and extremes
we get,6+12=18
We shall keep unit’s place digit(8) and carry forward ten’s place digit(1) to step 1.
988. Middle number is 8.
Step 4:Adding carry forward(1) from step 3 to step 1 answer, we get

9+1=10
Ans 32 X 34= 1088
Tip to remember this trick: Always keep in mind that whenever you get a 2 digit number on multiplication, the ten’s place digit is always carried forward to the number immediately to the left direction of it. 

Also Read
Shortcut to divide any 2 digit number by 5
Vedic math trick to check multiplication
3 digit multiplication trick in banking



Shortcut to Find Cube Root

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Shortcut to find cuberoot of any 5 or 6 digit number
Shortcut to find cube root of a number
Shortcut to find cube root is especially helpful in competitive exams where every second counts.
By using this method you can save a lot of time and also get accurate results.

Shortcut to find cube root of a number Mentally

Steps

Step 1:Find the cube root of the last digit.
Points to be remembered while using this method.
(1)If the last digit is 8 then cube root will be 2.
(2)If the last digit is 2 then cube root will be 8.
(3)If the last digit is 7 then cube root will be 3.
(4)If the last digit is 3 then cube root will be 7.
(5)If the last digit is any other digit other than 2,8,3,7 then put the same number.
From this step you will get the unit’s or one’s place digit.

To find the tenth place digit you need to follow the below steps.
Step 2:Strike out the last 3 digits of the given number.
Step3:Find the nearest cube of the remaining number.
Step 4:Find the cube root of the nearest cube which will give you ten’s place digit.


List of cubes to be memorized
13=1               43=64              73=343
23=8               53=125            83=512
33=27             63=216            93=729


NOTE: Shortcut to find cube root of any 5 or 6 digit number is applicable only if the given number is a perfect cube.
You can verify whether the given number is a perfect cube or not by using the Prime Factorization Method. If you are not familiar with this method check it here.

Cube root Shortcut of a 6 digit number

Let me explain this with an example to make things more clear and easy to understand.
So lets say we want to find the cube root of a 6 digit number 15746

Example 1:Find the cube root of 157464 in 5 seconds.
                ∛157464=?
Step 1:First we need to find the cube root of the last digit of the given number.
Here the last digit is 4 . 4 is a number other than 2, 8, 3, 7. Hence we put the number as it is.We get our one’s place digit as 4.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 464 which we will strike off as shown below
157464

Step 3: We need to find the nearest cube to the remaining number(157).We find that 125 is the nearest cube to 157.

Step 4: We need to find the cube root of the nearest cube(125)
∛125=5
From this step we get our ten’s place digit as 5.
From step 1 and step 4 we get the 
 ∛157464=54
Ans: Cube root of 157464 is 54

Example 2:Find the cube root of 110592 in 5 seconds.
                ∛110592=?
Step 1:First we need to find the cube root of the last digit of the given number.Here the last digit is 2 . As per table, we will consider 8 as the cube root of 2. We get our one’s place digit as 8.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 592 which we will strike off as shown below
110592

Step 3: We need to find the nearest cube to the remaining number(110).We find that 64 is the nearest cube to 110.

Step 4: We need to find the cube root of the nearest cube(64)
∛64=4
From this step we get our ten’s place digit as 4.
From step 1 and step 4 we get the 
 ∛110592=48
Ans: Cube root of 110592 is 48

Example 3:Find the cube root of 148877 in 5 seconds.
                ∛148877=?

Step 1:First we need to find the cube root of the last digit of the given number.Here the last digit is 7. As per table, we will consider 3 as the cube root of 7. We get our one’s place digit as 3.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 877 which we will strike off as shown below
148877

Step 3: We need to find the nearest cube to the remaining number(148).We find that 125 is the nearest cube to 148.

Step 4: We need to find the cube root of the nearest cube(64)
∛125=5
From this step we get our ten’s place digit as 5.
From step 1 and step 4 we get the 
 ∛148877=53
Ans:Cube root of 148877 is 53

More Examples

Example 4:Find the cube root of 328509 in 5 seconds.
                ∛328509=?
Step 1:First we need to find the cube root of the last digit of the given number. Here the last digit is 9.9 is a number other than 2, 8, 3, 7. Hence we put the number as it is.We get our one’s place digit as 9.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 509 which we will strike off as shown below
328509

Step 3: We need to find the nearest cube to the remaining number(328).We find that 216 is the nearest cube to 328.

Step 4: We need to find the cube root of the nearest cube(216)
∛216=6
From this step we get our ten’s place digit as 6.
From step 1 and step 4 we get the 
 ∛328509=69
Ans: Cube root of 328509 is 69

Example 5:Find the cube root of 636056 in 5 seconds.
                ∛636056=?
Step 1:First we need to find the cube root of the last digit of the given number. Here the last digit is 6.6 is a number other than 2, 8, 3, 7. Hence we put the number as it is.We get our one’s place digit as 6.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 056 which we will strike off as shown below
636056

Step 3: We need to find the nearest cube to the remaining number(636).We find that 512 is the nearest cube to 636.

Step 4: We need to find the cube root of the nearest cube(512)
∛512=8
From this step we get our ten’s place digit as 8.
From step 1 and step 4 we get the 
 ∛636056=86
Ans: Cube root of 636056 is 86

Cube root Shortcut of a 5 digit number

Now, that you have understood how to find cube root of a number within seconds 
lets see how this method works for a 5 digit number with the help of an example. Short cut to find Cube Root of  5 digit number is similar to finding cube root of 6 digit number.
Example 1:Find the cube root of 32768
                 ∛32768=?
Step 1: First,we need to find the cube root of the last digit of the given number. Here the last digit is 8.
∛8=2
We get the one’s place digit as 2.
Step 2: We need to strike out the last 3 digits of the given number.
In this example,768 are the last 3 digits which we we will strike off as shown below
32768
Step 3: We find that the nearest cube to the remaining number(32) is 27.
Step 4:  Now, we find that the cube root of 27
That will be  ∛27=3
From this step we get the ten’s place digit as 3. 
Therefore, from step 1 and step 2 we get 
∛32768=32
Ans:32

Example 2:Find the cube root of 19683 in 5 seconds.
                ∛19683=?

Lets go through the steps as below
Step 1:First we need to find the cube root of the last digit of the given number.Here the last digit is 3. As per table, we will consider 7 as the cube root of 3. We get our one’s place digit as 7.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 683 which we will strike off as shown below
19683

Step 3: We need to find the nearest cube to the remaining number(19).We find that 8 is the nearest cube to 19.

Step 4: We need to find the cube root of the nearest cube(64)
∛8=2
From this step we get our ten’s place digit as 2.
From step 1 and step 4 we get the 
 ∛19683=27
Ans:27

More Examples

Example 3:Find the cube root of 29791 in 5 seconds.
                ∛29791=?
Step 1:First we need to find the cube root of the last digit of the given number. Here the last digit is 1.1 is a number other than 2, 8, 3, 7. Hence we put the number as it is.We get our one’s place digit as 1.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 791 which we will strike off as shown below
29791

Step 3: We need to find the nearest cube to the remaining number(29).We find that 27 is the nearest cube to 29.

Step 4: We need to find the cube root of the nearest cube(216)
∛27=3
From this step we get our ten’s place digit as 3.
From step 1 and step 4 we get the 
 ∛29791=31
Ans:31

Example 4:Find the cube root of 91125 in 5 seconds.
                ∛91125=?

In this example, I am going to solve the question step by step.
Step 1:First we need to find the cube root of the last digit of the given number. Here the last digit is 5.5 is a number other than 2, 8, 3, 7. Hence we put the number as it is.We get our one’s place digit as5.

Now to get tenth place digit

Step 2: We need to strike the last 3 digits of the given number.
In this example the last 3 digits are 125 which we will strike off as shown below
91125

Step 3: We need to find the nearest cube to the remaining number(91).We find that 64 is the nearest cube to 91.

Step 4: We need to find the cube root of the nearest cube(216)
∛64=4
From this step we get our ten’s place digit as 4.
From step 1 and step 4, we get the 
 ∛91125=45
Ans: Cube root of 91125 is 45

Shortcut to square any number from 30 to 79

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Shortcut to square any number from (30-79)
Shortcut to square any number from 30 to 79 mentally in seconds is now possible for all aspiring candidates writing different competitive exams. It is always better to have some math tricks handy when you are planning to take any arithmetic aptitude test either in the competitive exams such as Bank exams,CAT,MAT.
Another easy trick to find square of the numbers between 30 to 79 is to take a common base as 50 and see how far the number is from 50.This method works well when the number is very close to 50.

Shortcut to square of number from 30 to 79 steps

Step 1:Find how many more or less the given number is from 50.

Step 2:Add the number to 25 if more than 50 or subtract the number from 25 if less than 50.

Step 3:Then find the square of the number added or subtracted and put next to the result arrived at in step 2.

Let us now apply the trick that we learnt in the example below

Examples

Example 1:Find the square of 52 in 5 seconds
52²=?
Step 1: We see that the given number is 2 more than 50.
52-50=2
Step 2: Here we notice that the given number is more than 50 so we add 25 as follows
25+2=27
Step 3: Now we find the square of  the number added(2)
22=4
putting the result obtained in step 3 next to the result obtained in step 2 after adding a 0 before it as it is a single digit,
we get, 2704

Ans: 52²=2704

Example 2:Find the square of 37 in 5 seconds.
37²=?
Step 1: We see that the given number is 13 less than 50
that is 50-37=13
Step 2: Here we notice that the given number is less than 50 so we subtract 25 as follows
25-13=12
Step 3: Now we find the square of  the number subtracted(13)
we get, 132=169
put the result obtained in step 3 next to the result obtained in step 2 as shown below. And carry forward hundreth place digit to step 2.
we get,1269

Step 4:Add carry forward from step 3 to result obtained in step 2.

we get, 12+1=13

Ans:       37²=1369 

Example 3:Find the square of 54 in 5 seconds
54²=?
Step 1: We see that the given number is 4 more than 50.
54-50=4
Step 2: Here we notice that the given number is more than 50 so we add 25 as follows
25+4=29
Step 3: Now we find the square of  the number added(4)
42=16
putting the result obtained in step 3 next to the result obtained in step 2
we get, 2916

Ans: 54²=2916

See how quickly you can square 54,49,53,51,48,32,57,59,64,67,72.Give it a try….


Also Read
Shortcut to square any number from 20-29
Shortcut to square any number from 10-19