Question

I'm not sure what I'm doing wrong in simplifying this square root. I'm factoring out 32 which is 2x2x2x2x2, In this there is 1 set of 5 so I thought the answer would be 1. However, my calculator is telling me its the answer is 2. What did I do wrong?


`\sqrt[5]{32}`

Answer 1

2

Explanation:

note that 2^{5} = 2 × 2 × 2 × 2 × 2 = 32, hence

\sqrt[5]{32} = \sqrt[5]{2^{5} } = (2^{5})^{\frac{1}{5} } = 2^{1} = 2

Answer 2

see explanation

Explanation:

note that
`2^(5)` = 2 × 2 × 2 × 2 × 2 = 32, hence

`\sqrt[5]{32}` =
`\sqrt[5]{2^(5) }` =
`(2^(5))^{(1)/(5) }` =
`2^(1)` = 2