Question

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

Answer 1

Answer:

64 is correct answer of your question.

Step-by-step explanation:

64 is a perfect square of 8 and also

64 is a perfect cube of 4.

Answer 2

Question :

Which of the following is both a perfect square and a perfect cube?

a.16

b.64

c.125

d.144

Answer :

Option b.64 is correct.

64 is both a perfect square and a perfect cube.

Given :

The options : 16 , 64 , 125 and 144

To find :

The number which is both a perfect square and a perfect cube

Solution :

Factors of 16 : 1, 2 , 4 , 8 , 16

16 = 2 × 2 × 2 × 2

16 = 2^4

or, 16 = 4^2

Factors of 64 : 1,2,4,8,16,32,64

64 = 2 × 2 × 2 × 2 × 2 × 2

64 = 2^6

Or, 64 = 8^2

Or, 64 = 8^2Or, 64 = 4^3

Factors of 125 : 1, 5 , 25, 125

125 = 5 × 5 × 5

125 = 5^3

Factors of 144 : 1,2,3,4,6,8,9,12,16,18,24,36,48,72, 144

144 = 2 × 2 × 2 × 2 × 3 × 3

144 = 2^4 × 3^2

Or, 144 = 12^2

Hence, we conclude that 64 is both a perfect square and a perfect cube.

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