## Saturday, October 22, 2011

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

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.

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
13=1               43=64              73=343
23=8               53=125            83=512
33=27             63=216            93=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

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:54

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

Example 2: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

Hence, from step 1 and step 2 we get
∛32768=32

Ans:32