Question

Please help!! Write in simplest radical form: √7/8 Show how you figured it out

Answer 1

Given expression: $\sqrt{\frac{7}{8}}$.

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

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

$\sqrt{8}=\sqrt{2^2\cdot \:2}=2\sqrt{2}$

$\frac{\sqrt{7}}{\sqrt{8}} =\frac{\sqrt{7}}{2\sqrt{2}}$

$\mathrm{Rationalize\:}\frac{\sqrt{7}}{2\sqrt{2}}$

$\mathrm{Multiply\:by\:the\:conjugate}\:\frac{\sqrt{2}}{\sqrt{2}}$

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

$=\frac{\sqrt{14}}{4}$

$=\frac{\sqrt{14}}{4}$.