Question

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

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{2}$

To rationalize the denominator, we multiply the fraction $\frac{4}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ (since $\frac{\sqrt{2}}{\sqrt{2}} = 1$ and multiplying by 1 doesn't change the value of the fraction). So we get $\frac{4\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}$.

Step2: Simplify the denominator

We know that $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$. So $\sqrt{2}\times\sqrt{2} = 2$. The fraction now becomes $\frac{4\sqrt{2}}{2}$.

Step3: Simplify the fraction

Divide the numerator and the denominator by their greatest common divisor, which is 2. $\frac{4\sqrt{2}\div2}{2\div2}=\frac{2\sqrt{2}}{1}=2\sqrt{2}$.

Answer:

$2\sqrt{2}$