Question

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HeRe'S yOuR QuEsTiOn

Find the smallest natural number by which 5184 should be multiplied so that the product is a perfect cube. ​

Answer 1

❇ANSWER❇

The number 5184 is already a perfect cube of 36.

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Answer 2

Find the prime factors:

5184 = 2 x 34

Find k:

5184 = = 20 x 34

For it to be a perfect cube, the exponents must be in

the multiple of 3s

5184k = 20 x 30

Therefore k = 3² = 9

Find the number:

The number = 5184 x 9 = 46656

Find the cube root:

46656 = 26 x 36

Divide the exponent by 3 to get the cube root:

46656 2² x 3² = 4 x 9 = 36

Answer: The smallest number to be multiplied is 9 and the cube root of the perfect cube is 36.