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