To Find if the Given Number is a Perfect Cube


How to find if the given number is a perfect cube?

If the prime factors of a number are grouped in triples of equal factors, then that number is called a perfect cube.

Examples to find if the given number is a perfect cube:

1. Find out if the following are perfect cubes.


(i) 250

(ii) 5832

(i) 250


Solution:

Resolving 250 as the product of prime factors

Perfect Cube


250 = 2 × 5 × 5 × 5

Since 2 does not exist in product of triples. 

Therefore, 250 is not a perfect cube. 





(ii) 5832

Solution:

Resolving 5832 as the product of prime factors

Perfect Cube


5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Since, they are grouped in triples.

Therefore, 5832 is a perfect cube.



2. Find the smallest number by which 1944 must be multiplied so that the product is a perfect cube.

Solution:


Resolving 1944 as the product of prime factors

Perfect Cube


1944 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3

In order to make 1944 a perfect cube, it must be multiplied by 3.



3. Find the smallest number by which 4394 must be divided so that the quotient is a perfect cube.

Solution:


Resolving 4394 as the product of primes

Perfect Cube


4394 = 2 × 13 × 13 × 13

In order to make 4394 a perfect cube, it must be divided by 2, so that the quotient is 2197.


 Cube and Cube Roots

Cube

To Find if the Given Number is a Perfect Cube

Cube Root

Method for Finding the Cube of a Two-Digit Number

Table of Cube Roots


 Cube and Cube Roots - Worksheets

Worksheet on Cube

Worksheet on Cube and Cube Root

Worksheet on Cube Root












8th Grade Math Practice 

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