Question

rationalize the denominator and simplify.
\frac{8}{\sqrt{7}}

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $\sqrt{7}$:
$\frac{8}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}}$

Step2: Simplify the expression

Calculate numerator and denominator:
$\frac{8\sqrt{7}}{\sqrt{7} \times \sqrt{7}} = \frac{8\sqrt{7}}{7}$

Answer:

$\frac{8\sqrt{7}}{7}$