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Question

Is 1188 a perfect cube number? If not by which smallest natural number should 1188 be divided so that the quotient is a perfect cube number. Also find the cube root of the new cube number.

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Solution

The prime factorisation of 1188 is1188 = 2×2×3×3×3×11Since the prime factor 2 and 11 do not occurr in the group of 3, so 1188 is not a perfect cube.Now, to make 1188 a perfect cube, it must be divided by 2×2×11 that is 44.Now, 1188 ÷ 44 = 27 a perfect cube numberNow, 273 = 3×3×33 = 3

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