Q102 of 142 Page 88

By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

Given: 3600

Factors of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5


As we see, 2,3 and 5 do not have a pair to make a cube.


Hence 3600 should be multipled with 2 × 2 × 3 × 5 to get perfect cube.


⇒ 3600 should multiply with 60.


Now, 3600× 60 = 216000


Now, 216000 is a perfect cube and the cube root is 2 × 2 × 3 × 5 i.e. 60.


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