Question

Rationalize $\sqrt{\frac{4+\sqrt{15}}{2\sqrt{2}}}\times \frac{22}{2\sqrt{2}}$

Answer 1

$\sqrt{\frac{4+\sqrt{15}}{2\sqrt{2}}}\times \frac{22}{2\sqrt{2}}$

$=\sqrt{\frac{4+\sqrt{15}}{2\sqrt{2}}}\times \frac{11}{\sqrt{2}}$

$=\frac{11\times \frac{\sqrt{4+\sqrt{15}}}{2^{\frac{3}{4}}}}{\sqrt{2}}$

$=\frac{11\sqrt{4+\sqrt{15}}}{2^{\frac{5}{4}}}$

$=\frac{11\sqrt{4+\sqrt{15}}}{2\times \sqrt[4]{42}}$

$=\frac{11\times 2^{\frac{3}{4}}\sqrt{4+\sqrt{15}}}{4}$