Question

question
express in simplest radical form.
\\(\frac{\sqrt{16}}{\sqrt{8}}\\)

Explanation:

Step1: Simplify the square roots

We know that $\sqrt{16} = 4$ and $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$. So the expression becomes $\frac{4}{2\sqrt{2}}$.

Step2: Simplify the fraction

Simplify $\frac{4}{2\sqrt{2}}$ by dividing the numerator and the denominator by 2, we get $\frac{2}{\sqrt{2}}$.

Step3: Rationalize the denominator

To rationalize the denominator, multiply the numerator and the denominator by $\sqrt{2}$, so $\frac{2\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{2\sqrt{2}}{2}$.

Step4: Simplify the fraction

Simplify $\frac{2\sqrt{2}}{2}$ by dividing the numerator and the denominator by 2, we get $\sqrt{2}$.

Answer:

$\sqrt{2}$