Question

by what least number should 8232 should be multiplied to become a perfect cube? also find the cube root of the product obtained

Answer 1

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Answer 2

Concept

Prime Factorization "finds out which key numbers are repeated together to form a real number.

Given

The number 8232 is not a perfect cube

Find

We have to find which number should be multiplied with 8232 so that it became perfect cube and also find out cube root of product

Solution

• By finding prime factors of 8232, 8232 =have 2*2*2*3*7*7*7
• For any number to be perfect cube their prime factors should be in pairs of 3
• Hence, 8232 = (2 * 2 * 2) * 3 * (7 * 7 * 7)
• So from this we can conclude that 3 should be multiplied 2 times with 8232 to became a perfect cube
• So, 8232 * 3*3 = (2 * 2 * 2) * (3 * 3 * 3) * (7 * 7*7)
• 74088 = (2 * 2 * 2) * (3 * 3 * 3) * (7 * 7*7)
• By prime factorization the cube root of 74088 will be 2*3*7 which will be 42

Hence 9 should should be multiplied with 8232 so that it became perfect cube and cube root of product will be 42

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