Which of the following is equal to the square root of the cube root of 5?
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

Solution:

Given, square root of the cube root of 5

The expression can be written as \(\sqrt{(\sqrt[3]{5})}\)

Now, \(\sqrt{(\sqrt[3]{5})}\) = \(((5)^{\frac{1}{3}})^{\frac{1}{2}}\)

= \((5)^{\frac{1}{6}}\)

From the option,

1) 5 to the power of 1 over 3

The expression can be written as \((5)^{\frac{1}{3}}\)

So, option(1) is not true.

2) 5 to the power of 1 over 6

The expression can be written as \((5)^{\frac{1}{6}}\)

So, option(2) is true.

3) 5 to the power of 2 over 3

The expression can be written as \((5)^{\frac{2}{3}}\)

So, option(3) is not true.

4) 5 to the power of 3 over 2

The expression can be written as \((5)^{\frac{3}{2}}\)

So, option(4) is not true.

Therefore, the square root of the cube root of 5 = \((5)^{\frac{1}{6}}\).

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Which of the following is equal to the square root of the cube root of 5?

Summary:

The square root of the cube root of 5 is equal to \((5)^{\frac{1}{6}}\).