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

Answer: Second Option

5 to the power of 1 over 6

Step-by-step 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

$\sqrt[n]{x^h}=x^{\frac{h}{n}$

So we have that:

$\sqrt[6]{5}=5^{\frac{1}{6}}$

The answer is the second option

5 to the power of 1 over 6