Question

using the work shown, what is \\(\frac{sqrt3{4}}{sqrt{2}}\\) in simplest radical form? 2 \\(sqrt{2^6}\\) \\(sqrt6{2}\\)

Explanation:

Step1: Rewrite radicals as exponents

$\frac{\sqrt[3]{4}}{\sqrt{2}} = \frac{4^{\frac{1}{3}}}{2^{\frac{1}{2}}}$

Step2: Express 4 as $2^2$

$\frac{(2^2)^{\frac{1}{3}}}{2^{\frac{1}{2}}} = \frac{2^{\frac{2}{3}}}{2^{\frac{1}{2}}}$

Step3: Subtract exponents (division rule)

$2^{\frac{2}{3}-\frac{1}{2}} = 2^{\frac{4}{6}-\frac{3}{6}} = 2^{\frac{1}{6}}$

Step4: Rewrite as radical form

$2^{\frac{1}{6}} = \sqrt[6]{2}$

Answer:

$\sqrt[6]{2}$