Question

express in simplest form with a rational denominator.
\\(\dfrac{1}{\sqrt{2}}\\)

Explanation:

Step1: Rationalize the denominator

To rationalize the denominator of \(\frac{1}{\sqrt{2}}\), we multiply the numerator and the denominator by \(\sqrt{2}\) because \(\sqrt{a}\times\sqrt{a}=a\) (here \(a = 2\)). So we have:

$$ \frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}} $$

Step2: Simplify the expression

Simplify the denominator \(\sqrt{2}\times\sqrt{2}=\sqrt{2\times2}=\sqrt{4} = 2\). The numerator is \(1\times\sqrt{2}=\sqrt{2}\). So the expression becomes \(\frac{\sqrt{2}}{2}\).

Answer:

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