Question

What is the smallest number by which 3600 must be divided so that the quotient obtained will be perfect cube?​

Answer 1

Step-by-step explanation:

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Given:

What is the smallest number by which 3600 must be divided so that the quotient obtained will be perfect cube?

To Find:

The smallest number by which 3600 must be divided so that the quotient obtained will be perfect cube.

Solution:

By prime factorizing 3600, we get:

3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

By forming groups in triplet of equal factors we get, 3600 = (2 × 2 × 2) × (3 × 3) × (5 × 5) × 2

Since, 2, 3 and 5 cannot form a triplet of equal factors.

Therefore, 3600 must be multiplied with 60 (2 × 2 × 3 × 5) to get a perfect cube.

3600 × 60 = 216000

Cube root of 216000 is

∛216000 = ∛ (60 × 60 × 60)

∛216000 = ∛ (603) = 60

Therefore, the smallest number which when multiplied with 3600 makes a perfect cube is 60.

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