Question

Which of the following is equal to the square root of the cube root of 5 ? (1 point)

5 to the power of 1 over 3

5 to the power of 1 over 6

5 to the power of 2 over 3

5 to the power of 3 over 2

Answer 1

5 to the power of 1 over 6

Explanation:

Answer 2

Answer: Second Option

5 to the power of 1 over 6

Explanation:

The square root of the cubic root of 5 is written as follows

`\sqrt[2]{\sqrt[3]{5}}`

Now use the following property of the roots

`\sqrt[m]{\sqrt[n]{x}}=\sqrt[m*n]{x}`

In this case
`m = 2` and
`n=3` and
`x=5`

So we have that

`\sqrt[2]{\sqrt[3]{5}}=\sqrt[2*3]{5}`

`\sqrt[2*3]{5}=\sqrt[6]{5}`

Now use the following property

`\sqrt[n]{x^h}=x^{(h)/(n)`

So we have that:

`\sqrt[6]{5}=5^{(1)/(6)}`

The answer is the second option

5 to the power of 1 over 6