Question

question
express in simplest form with a rational denominator.
\\(\frac{7}{\sqrt{8}}\\)
answer attempt 1 out of 10
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Explanation:

Step1: Simplify the square root in the denominator

First, we simplify $\sqrt{8}$. We know that $8 = 4\times2$, and $\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}=2\sqrt{2}$. So, the expression $\frac{7}{\sqrt{8}}$ becomes $\frac{7}{2\sqrt{2}}$.

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by $\sqrt{2}$. This is because when we multiply $\sqrt{2}$ with $\sqrt{2}$, we get $2$ (a rational number). So, we have:

$$ \frac{7}{2\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{7\sqrt{2}}{2\times2}=\frac{7\sqrt{2}}{4} $$

Answer:

$\frac{7\sqrt{2}}{4}$