Answer
5 to the power of 1 over 6
or as an expression: \(5^{\frac{1}{6} }\)
Explanation
First we are going to express our statement as an algebraic expression:
square root of the cube root of 5 = \(\sqrt{\sqrt[3]{5} }\)
Next, we are using laws of radicals to simplify our expression:
Law of radicals: \(\sqrt[m]{\sqrt[n]{a} } =\sqrt[mn]{a}\)
We can infer from our expression that n=2, m=3, and a=5, so lets replace the values:
\(\sqrt{\sqrt[3]{5} }=\sqrt[(2)(3)]{5} =\sqrt[6]{5}\)
Now, to express the radical as exponent, we are going to use another law of radicals:
Law of radicals: \(\sqrt[n]{a} =a^{\frac{1}{n} }\)
Just like before, we can infer for our expression that n=6 and a=5, so let's replace the values:
\(\sqrt[6]{5} =5^{\frac{1}{6} }\)
And in words:
square root of the cube root of 5 is equal to 5 to the power of 1 over 6
