Question

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

• A. 343
• B. 36
• C. 216
• D. 64

Answer 1

The correct option is D 64

We know that 64 can be written as $2\times 2\times 2\times 2\times 2\times 2⟹\sqrt[2]{264}=\sqrt[2]{2\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{2\times 2}}=2\times 2\times 2=8$
And,
$\sqrt[3]{364}=\sqrt[3]{3\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}}=2\times 2=4$
$⟹$ 64 is both perfect square and perfect cube number.