Question

Simplify the expression into an equivalent radical expression.

Answer 1

`\huge \sqrt[6]{5}`

Step-by-step explanation:

We can simplify the radical expression:

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

by rewriting the radicals as exponents:

`\left(5^(1/3)\right)^(1/2)`

Then, we can simplify using the power to a power exponent rule:

`\displaystyle 5^{\left(\!(1)/(3)\cdot (1)/(2)\!\right)}`

`\displaystyle \implies 5^(1/6)`

Finally, we can rewrite it again as a radical:

`\huge\boxed{\sqrt[6]{5}}`

Further Note

We can check our answer by plugging both the given and manipulated values into the calculator. Both yield approximately 1.307.