Question

Find the smallest number by which 8232 must be multiplied so that the product is perfect cube?
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Answer 1

Answer:

9

Step-by-step explanation:

Firstly, we have to prime factorize 8232.

8232 = 2 x 2 x 2 x 3 x 7 x 7 x 7

Since 3 and 3 does not exist in a pair, 3 and 3  needs to be multiplied.

= 8232 x 3 x 3

= 8232 x 9

= 74088 (Perfect cube)

So, 9 is the smallest number that needs to be multiplied to make 8232 a perfect cube.

Hope it helps you!

Answer 2

Solution :-

Finding prime factors of 8232 we get,

→ 8232 = 2 * 2 * 2 * 3 * 7 * 7 * 7

now, we know that, for a number to be perfect cube , prime factors should be in pair of 3 .

So,

→ 8232 = (2 * 2 * 2) * 3 * (7 * 7 * 7)

as we can see that, 3 appears only 1 time . Therefore, we can conclude that, in order to make it perfect cube we must need 2 times of 3 .

therefore,

→ 8232 * 3 * 3 = (2 * 2 * 2) * (3 * 3 * 3) * (7 * 7 * 7)

→ 8232 * 9 = (2 * 2 * 2) * (3 * 3 * 3) * (7 * 7 * 7)

→ 74088 = (2 * 2 * 2) * (3 * 3 * 3) * (7 * 7 * 7)

Hence, the smallest number by which 8232 must be multiplied so that the product is perfect cube is equal to 9 .

Extra :- Also the required perfect cube number will be 74088 and its cube root will be 2 * 3 * 7 = 42 .

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