# Shortcut to Find Cube Root

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

### 0 thoughts on “Shortcut to Find Cube Root”

1. can you tell me how would you use your method to find out the cube root of 80000?

2. while calculating the cube root of 103823, iam getting 57
as the ans. considering 125 as nearest cube to 103 but (47)^3 =103823 which one
is correct

• I think you have to look for the nearest cube less than that number.. ie. for 103 it will be 64.

• suneetha: u need to consider a number whose cube is less then then given question

eq > cube root of 19823

see cube of 3 is 27
cube of 2 is 8
827
ans : cube root of 27
since it lies between cube of 2 and 3 , just stick to lower number i.e 2

• by the said method it comes as 47 only and not 57. redo sir.

3. very useful tip, keep posting..