Question

Which of the following is both a perfect square and a perfect cube? 16 64 125 144

Answer 1

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125 and 64 is the both a perfect square and a perfect cube.

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Square root of 125 = 15

cube root of 125 = 5

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square root of 64 = 8

cube root of 64 = 4

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Answer 2

Among the given options option (2) 64 is both a perfect square and a perfect cube of 8 and 4.

Concept used :

Perfect square:

If all the prime factors of a natural number can be paired then it is a perfect square.

Perfect cube :

A given natural number is a perfect cube if it can be expressed as the product of triples of equal factors.

Solution:

(1) 16 is not a perfect cube it is a perfect square of 4 = $(4 \times 4) = 4^2 = 16$.

(2) 64 is both a perfect square and a perfect cube of 8 and 4 = $(8 \times 8) = 8^2 = 64 , (4\times 4 \times 4) = 4^3 = 64.$

(3) 125 is not a perfect square it is a perfect cube of 5 = $(5 \times 5 \times 5) = 5^3 = 125.$

(4) 144 is not a perfect cube it is a perfect square of 12 =$(12 \times 12) = 12^2 = 144.$

Hence, option (2) 64 is both a perfect square and a perfect cube of 8 and 4.

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