Question

question
express in simplest form with a rational denominator.
\\(\frac{4}{\sqrt{2}}\\)

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 non - negative real number $a$).
So we have $\frac{4\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}$.

Step2: Simplify the expression

First, calculate the denominator: $\sqrt{2}\times\sqrt{2} = 2$.
Then, the numerator is $4\times\sqrt{2}=4\sqrt{2}$.
So the expression becomes $\frac{4\sqrt{2}}{2}$.

Step3: Simplify the fraction

We can simplify $\frac{4\sqrt{2}}{2}$ by dividing the coefficient of the numerator by the denominator. $4\div2 = 2$, so the simplified form is $2\sqrt{2}$.

Answer:

$2\sqrt{2}$