Estimating Cube Root

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 = 3 6 ).

 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 ---> 238328

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 6 3 =216 and 7 3 =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 ---> 175616

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 5 3 =125 and 6 3 = 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

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