Bank exam

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

Shortcut to square any number from 20 to 29

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Shortcut to square any number from(20-29)
Shortcut to square any number from 20 to 29 is an easy way to mentally square any number from 20 to 29. Knowing this trick can of great help especially when squaring a number forms part of a bigger question.
Below are the steps to find square of any number from 20 to 29 in seconds.

Step 1:First add the given number and the unit’s digit.
Step 2:Double the result obtained in step 1.
Step 3:Square the unit’s digit of the number given in question and place it next to the result obtained in step 2.

Examples

Example 1:Find the square of 22 in 5 seconds

22²=?

Step 1:Here the unit’s place digit is 2. Adding unit digit to the given number
we get,22 + 2=24
Step 2:Doubling the result in step1
we get, 24×2=48_
Step 3:Squaring the unit’ place digit
we get,22=4
Now put the result obtained in step 3 in step 2,we get

22²=484

Ans:484 

Example 2:Find the square of 28 in 5 seconds.
28²=?
Step 1:Here the unit’s place digit is 8. Adding unit digit to the given number

we get,28+8=36
Step 2: Doubling the result in step1

we get, 36×2=72_
Step 3:Squaring the unit’ place digit

we get, 82= 64
Put the result obtained in step 2,Now carry forward ten’s place digit(6) to step 2 .
Step 4: Add carry forward from step 3 to result obtained in step 2
we get, 72+6=78
Put the unit’s place digit(4) the derived from step 3 next to result obtained in step 4.
we get, 784
28²=784     

Ans:784

Example 3:Find the square of 23 in 5 seconds

23²=?

Step 1:Here the unit’s place digit is 3. Adding unit digit to the given number
we get,23 +3=26
Step 2:Doubling the result in step1
we get, 26×2=52_
Step 3:Squaring the unit’ place digit
we get,32=9
Now put the result obtained in step 3 in step 2,we get

23²=529

Ans:529

square number from 10 to 19 math trick

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square number from 10 to 19 math trick
Square number from 10 to 19 using this amazing shortcut. Learning new shortcuts is a way to ensure success in competitive exams. To have an edge over others you must ensure that you answer questions fast and with accuracy. Here are the steps to find square of number from 10 to 19 in seconds.

Step 1: First add the given number and the units digit and leave a blank .

Step 2: Then Square the unit’s digit and put the number next to the result obtained in Step 1.

Examples to find square of number from 10 to 19

As they say practice makes a man perfect. Practice the below examples to perfect your skill.
Example-1:Find the square of 13 in 5 seconds
13² = ?
Step 1: Here the unit’s place digit is 3, Adding unit’s place digit to the given number(13)
we get 13 + 3 = 16_
Step 2: Square the unit’s digit
We get, 32 = 9
put the result obtained in step 2 in step 1 we get
13²=169
Ans= 169

Example-2:Find the square of 16 in 5 seconds

16² = ?
Step 1:Here the unit’s place digit is 6, Adding unit’s place digit to the given number(16)
we get, 16 + 6 = 22_
Step 2: Square the unit’s digit

We get, 62 = 36
put the unit’s place digit(6) of the result obtained in step 2 in step 1 as shown below and carry forward ten’s place digit(3) to step 1
226
Step 3: Add carry forward(3) from step 2 to the result obtained in step 1 as below
22+3=25
16²=256
Ans=256
Example-3:Find the square of 14 in 5 seconds
14² = ?
Step 1: Here the unit’s place digit is 4, Adding unit’s place digit to the given number(14)
we get 14 + 4 = 17_
Step 2:Square the unit’s digit
We get, 42 = 16
put the unit’s place digit(6) of the result obtained in step 2 in step 1 as shown below and carry forward ten’s place digit(3) to step 1
176
Step 3: Add carry forward(1) from step 2 to the result obtained in step 1 as below
17+1=18
17²=186
Ans=186
Example-4:Find the square of 12 in 5 seconds
12² = ?
Step 1: Here the unit’s place digit is 2, Adding unit’s place digit to the given number(13)
we get 12 + 2 = 14_
Step 2: Square the unit’s digit
We get, 22 = 4
put the result obtained in step 2 in step 1 we get
12²=144
Ans= 144

How to square a number ending with 5 within seconds

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How to square a number ending with 5 within seconds
Squaring a number ending in 5 is the easiest if you know the trick.
Number given to you can be a two digit number or three digit number or five or six digit number, it does’n t matter. The same trick can be applied to find the square of any number ending in 5.

Square a number ending with 5 within seconds

Let us now discuss the steps to follow

Step 1:Multiply the ten’s digit of the given number with its immediate next number.This will be the 1st digit of the answer.

Step 2:Put 25 next to the result of step 1.
Logic behind putting 25 is that the number will always end with 5 and 5² is 25.

You get the answer

Examples to find square of a 2 digit number ending with 5

Let us find squares of numbers ending in 5 using this trick

Example 1:35²=?
Step 1: 3 is the ten’s digit in the given number 35.
Immediate next number to 3 is 4.
Hence,by multiplying 3 & 4 we get 12(3 x 4=12).which is the 1st digit of the answer.

Step 2: Now putting 25 next to 12 we get the answer as 1225.

Ans  35²= 1225

Example 2:25²=?
Step 1: 2 is the ten’s digit in the given number 25.
Immediate next number to 2 is 3.
Hence,by multiplying 2 & 3 we get 6(2 x 3=6).which is the 1st digit of the answer.

Step 2: Now putting 25 next to 6 we get the answer as 625.

Ans  25²= 625

Example 3:65²=?
Step 1: 6 is the ten’s digit in the given number 65.
Immediate next number to 6 is 7.
Hence,by multiplying 6 & 7 we get 42(6 x 7=42).which is the 1st digit of the answer.

Step 2: Now putting 25 next to 42 we get the answer as 4225.

Ans  65²= 4225

Now you try to square 25,45,15,55,65,75,85,95 & see how quickly you can square.

Examples to find square of a 3 digit number ending with 5

Example 1:125²=?
Step 1: 12 is the ten’s digit in the given number 125.
Immediate next number to 12 is 13.
Hence,by multiplying 12 & 13 we get 156(12 x 13=156).which is the 1st digit of the answer.

[To multiply a 2 digit by 2 digit number when ten’s digit of both numbers is 1 you can apply below trick to get your answer quickly.

1st digit =1
middle digit =add unit’s place digit of both numbers(2+3=5)
unit’s place digit=Multiply unit place digit of both numbers(2 x 3=6)]

Step 2: Now putting 25 next to 156 we get the answer as 15625.

Ans 125²= 15625

Example 2:135²=?
Step 1: 13 is the ten’s digit in the given number 135.
Immediate next number to 13 is 14.
Hence,by multiplying 13 & 14 we get 182(13 x 14=182).which is the 1st digit of the answer.

Step 2: Now putting 25 next to 182 we get the answer as 18225.

Ans 135²= 18225

Example 3:145²=?
Step 1: 14 is the ten’s digit in the given number 145.Immediate next number to 14 is 15.
Hence,by multiplying 14 & 15 we get 210(14 x 15=210).which is the 1st digit of the answer. Apply the below trick to multiply quickly
https://www.yobankexams.com/2014/01/shortcut-to-multiply-any-2-digit-number-by-15.html
Step 2: Now putting 25 next to 210 we get the answer as 21025.

Ans 145²= 21025

Now you try to square 105,115,135,145,155,165,175,185,195 & see how quickly you can square.