Question

Rewrite in simplest radical form sqrt x * sqrt[4] x each step of your process

Answer 1

I assume the given expression is

`\sqrt x \sqrt[4]{x}`

We can write each root as a rational power of x, then add the exponents:

`\sqrt x \sqrt[4]{x} = x^(\frac12) x^(\frac14) = x^(\frac12 + \frac14) = x^(\frac34)`

Then putting it back into radical form, we have

`\sqrt x \sqrt[4]{x} = \sqrt[4]{x^3}`