# Estimating Cube Root

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Estimating Cube Root, this method will work only if the given number is a perfect cube. The following are the steps to estimate the cube root.

Step I : Make groups of 3 digits from unit(one's) place.This the 1st group.The remaining number makes the 2nd group.

Step II : The unit's digit of the 1st group will decide the unit digit of the cube root.( if the unit digit of the cube is 6 then the unit digit of cube root will also 6 as 6 x 6 x 6 = 36).

Step III : Find the cube of numbers between which the 2nd group lie.

Step IV : Take the smaller number as its ten's digit.
 Unit digit of a given number Unit digit of cube root 1 1 3 7 4 4 5 5 6 6 7 3 8 2

Examples on estimating cube root :

1) Find the cube root of 238328.

Solution :
238328 is an even number so its cube root has to an even number.
Make two groups ---> 238 328

First group 328 ---> unit digit is 8 so unit digit of cube root will be 2.
(see the above table).

Second Group 238 -----> it lies between 63=216 and 73 =343 .

So take the smaller number 6 as ten's place.

∴ ∛238328 = 62
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2) Find the cube root of -175616.

Solution :
We know that ∛-175616 = - ∛175616

The number is even so its cube root has to an even number.

Make two groups ---> 175 616

First group 616 ---> unit digit is 6 so unit digit of cube root will be 6
(see the above table).

Second Group 175 -----> it lies between 53=125 and 63 = 216 .

So take the smaller number 5 as ten's place.

Cube and Cube Roots

Cube of Numbers
Perfect Cube
Properties of Cube
Cube by Column method
Cube of Negative numbers
Cube of Rational numbers
Cube Root
Finding cube root by Prime Factorization
Cube root of Rational numbers
Estimating cube root

From estimation of cube root to Exponents