Question

this is the only question in this section
question
express in simplest form with a rational denominator.
\\(\frac{1}{\sqrt{2}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Rationalize the denominator

To rationalize the denominator of $\frac{1}{\sqrt{2}}$, we multiply the numerator and the denominator by $\sqrt{2}$ (since multiplying a square root by itself gives a rational number). So we have:
$\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}$

Step2: Simplify the expression

Simplify the denominator: $\sqrt{2}\times\sqrt{2} = 2$ (by the property $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$). The numerator is $\sqrt{2}$. So the expression becomes $\frac{\sqrt{2}}{2}$.

Answer:

$\frac{\sqrt{2}}{2}$