Question

question
express in simplest form with a rational denominator.
\\(\frac{4}{\sqrt{2}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Rationalize the denominator

To rationalize the denominator of $\frac{4}{\sqrt{2}}$, we multiply the numerator and the denominator by $\sqrt{2}$ (since $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$). So we have:
$\frac{4\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}$

Step2: Simplify the expression

First, simplify the denominator: $\sqrt{2}\times\sqrt{2} = 2$. Then the numerator is $4\sqrt{2}$. So the fraction becomes $\frac{4\sqrt{2}}{2}$. Now, simplify the fraction by dividing 4 by 2: $\frac{4\sqrt{2}}{2}=2\sqrt{2}$.

Answer:

$2\sqrt{2}$