Question

express in simplest form with a rational denominator.
\\(\frac{3}{\sqrt{18}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify \(\sqrt{18}\). We know that \(18 = 9\times2\), and \(\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}\) (since \(\sqrt{9} = 3\)). So the expression becomes \(\frac{3}{3\sqrt{2}}\).

Step2: Simplify the fraction

Now, we can simplify \(\frac{3}{3\sqrt{2}}\). The 3 in the numerator and the 3 in the denominator cancel out, leaving us with \(\frac{1}{\sqrt{2}}\). But we still have a radical in the denominator, so we rationalize the denominator by multiplying the numerator and the denominator by \(\sqrt{2}\).

So, \(\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}\) (because \(\sqrt{2}\times\sqrt{2}=2\)).

Answer:

\(\frac{\sqrt{2}}{2}\)