Rationalize the denominator: $\sqrt{\frac{3}{8}}.$
We have $$\sqrt{\frac{3}{8}} = \frac{\sqrt{3}}{\sqrt{8}} = \frac{\sqrt{6}}{\sqrt{16}} = \boxed{\frac{\sqrt{6}}{4}}.$$
\frac{\sqrt{6}}{4}
Level 3
Algebra
Problem: Rationalize the denominator: $\sqrt{\frac{3}{8}}.$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To rationalize the denominator of the expression $\sqrt{\frac{3}{8}}$, first recognize that the denominator is a whole number. The goal is to eliminate the square root from the denominator. 

Start by rewriting the expression as $\frac{\sqrt{3}}{\sqrt{8}}$. Next, simplify $\sqrt{8}$, which can be expressed as $\sqrt{4 \cdot 2}$. This simplifies to $\sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$. 

Now, substitute this back into the expression: $\frac{\sqrt{3}}{\sqrt{8}} = \frac{\sqrt{3}}{2\sqrt{2}}$. 

To rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{2}$. This gives:

Numerator: $\sqrt{3} \cdot \sqrt{2} = \sqrt{6}$.

Denominator: $2\sqrt{2} \cdot \sqrt{2} = 2 \cdot 2 = 4$.

Thus, the expression becomes $\frac{\sqrt{6}}{4}$. 

This final form has a rational denominator, achieving the goal of rationalization. The answer is $\frac{\sqrt{6}}{4}$.<|END_OF_LATENT|> The final answer is $\frac{\sqrt{6}}{4}$.