Question

Find the smallest number by which 675 must be multiplied to get a perfect cube.​

Answer 1

Answer:

We have 675 = 3 × 3 × 3 × 5 × 5

Grouping the prime factors of 675 to triples, we are left over with 5 × 5.

∴ 675 is not a perfect cube.

Now, [675] × 5 = [3 × 3 × 3 × 5 × 5] × 5

or 3375 = 3 × 3 × 3 × 5 × 5 × 5

Now, 3375 is a perfect cube.

Thus, the smallest required number to multiply 675 such that the new number perfect cube is 5.

Step-by-step explanation:

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