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.

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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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