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.

Step 4:Find the cube root of the nearest cube which will give you ten’s place digit.

__List of cubes to be memorized__1

^{3}=1 4

^{3}=64 7

^{3}=343

2

^{3}=8 5

^{3}=125 8

^{3}=512

3

^{3}=27 6

^{3}=216 9

^{3}=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.

**5.**

**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

110~~592~~

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

**4.**

**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

148~~877~~

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

**5.**

**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

328~~509~~

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

**6.**

**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

636~~056~~

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

**8.**

**86**

**Ans: Cube root of 636056 is 86**

## Cube root Shortcut of a 5 digit number

**2.**

**3.**

**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

19~~683~~

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

**2.**

**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

29~~791~~

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

**3.**

**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 as**5**.

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

91~~125~~

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

**4.**

**45**

**Ans: Cube root of 91125 is 45**

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

VERY NICE TIPS

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.

very useful tip, keep posting..

thanks .. but i can’t seem to find a method for finding cube root for any general number which is not a perfect cube of a natural number (e.g. 32770). In this case, the above algorithm does not provide even an approximately good solution.

79509 PLS FIND ITS CUBE ROOT AND EXPLN ANS

sir not getting exact value of cube root of the no u given

pls find the cube root of 10239

Shortcut to find cube root value https://www.youtube.com/watch?v=KS9IC995QDw