Question

question
express in simplest form with a rational denominator.
\\(\frac{5}{\sqrt{27}}\\)

answer attempt 2 out of 10

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{27}$. We know that $27 = 9\times3$, and $\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}$. So the expression becomes $\frac{5}{3\sqrt{3}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{3}$.
So we have $\frac{5\times\sqrt{3}}{3\sqrt{3}\times\sqrt{3}}$.
Since $\sqrt{3}\times\sqrt{3}=3$, the denominator becomes $3\times3 = 9$, and the numerator becomes $5\sqrt{3}$.
So the expression simplifies to $\frac{5\sqrt{3}}{9}$.

Answer:

$\frac{5\sqrt{3}}{9}$