# Shortcut to find cuberoot of any 5 or 6 digit number

By using this method you can save a lot of time and also get accurate results.

__Shortcut to mentally find the cube root of any 5 or 6 digit number__

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 3: 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__

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 cuberoot 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.

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

**5.**

**54**

**Ans:54**

**2.**

**3.**

**32**

**Ans:32**

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