Question

question
express in simplest form with a rational denominator.
\\(\frac{5}{\sqrt{24}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{24}$. We can factor 24 as $4\times6$, and since $\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$, so $\sqrt{24} = 2\sqrt{6}$. Now our expression becomes $\frac{5}{2\sqrt{6}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{6}$. So we have $\frac{5\times\sqrt{6}}{2\sqrt{6}\times\sqrt{6}}$.

Step3: Simplify the denominator

Simplify the denominator: $\sqrt{6}\times\sqrt{6}=6$. So now the expression is $\frac{5\sqrt{6}}{2\times6}=\frac{5\sqrt{6}}{12}$.

Answer:

$\frac{5\sqrt{6}}{12}$