Question

rationlize the denominator: 4/2+sqrt2+sqrt7..............pls...help

Answer 1

\[\frac{4}{2 + \sqrt{2} + \sqrt{7}}\]

Is this the question ??

Answer 2

yes

Answer 3

\[\frac{4}{2 + \sqrt{2} + \sqrt{7}} \times \frac{2 + \sqrt{2} - \sqrt{7}}{2 + \sqrt{2} - \sqrt{7}} \implies \frac{8 + 4\sqrt{2} - 4 \sqrt{7}}{(2 + \sqrt{2})^2 - 7}\]

Answer 4

\[\frac{8 + 4\sqrt{2} - 4 \sqrt{7}}{-1 + 4 \sqrt{2}} \times \frac{4 \sqrt{2} + 1}{4 \sqrt{2} + 1} \implies \frac{40 + 36 \sqrt{2}-4 \sqrt{7} - 16 \sqrt{14}}{31}\]