Question

express in simplest form with a rational denominator.
\\(\frac{6}{\sqrt{18}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Simplify the denominator

Simplify $\sqrt{18}$. We know that $18 = 9\times2$, so $\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$. Now the expression becomes $\frac{6}{3\sqrt{2}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{2}$. So we have $\frac{6\times\sqrt{2}}{3\sqrt{2}\times\sqrt{2}}$.

Step3: Simplify the expression

Simplify the numerator and the denominator. The numerator is $6\sqrt{2}$, and the denominator is $3\times2 = 6$ (since $\sqrt{2}\times\sqrt{2}=2$). Then $\frac{6\sqrt{2}}{6}=\sqrt{2}$.

Answer:

$\sqrt{2}$