Question

question
express in simplest form with a rational denominator.
\\(\frac{4}{\sqrt{54}}\\)
answer attempt 1 out of 10
submit answer

Explanation:

Step1: Simplify the square root

First, we simplify $\sqrt{54}$. We factor 54: $54 = 9 \times 6$, and since $\sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}$. So the expression becomes $\frac{4}{3\sqrt{6}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and denominator by $\sqrt{6}$:

$$ \frac{4 \times \sqrt{6}}{3\sqrt{6} \times \sqrt{6}} = \frac{4\sqrt{6}}{3 \times 6} = \frac{4\sqrt{6}}{18} $$

Step3: Simplify the fraction

We can simplify $\frac{4\sqrt{6}}{18}$ by dividing the numerator and denominator by 2:

$$ \frac{2\sqrt{6}}{9} $$

Answer:

$\frac{2\sqrt{6}}{9}$