Question

simplify root7 + root 2 upon 9+2 root 14

Answer 1

Answer:

$\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}=\frac{\sqrt{7}-\sqrt{2}}{5}$

Step-by-step explanation:

we are given $\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}$

We simplify it by rationalizing the denominator,

$\implies\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}\times\frac{9-2\sqrt{14}}{9-2\sqrt{14}}$

$\implies\frac{(\sqrt{7}+\sqrt{2})(9-2\sqrt{14})}{9^2-(2\sqrt{14})^2}$

$\implies\frac{\sqrt{7}(9-2\sqrt{14})+\sqrt{2}(9-2\sqrt{14})}{81-4\times14}$

$\implies\frac{9\sqrt{7}-14\sqrt{2}+9\sqrt{2}-4\sqrt{7}}{81-56}$

$\implies\frac{5\sqrt{7}-5\sqrt{2}}{25}$

$\implies\frac{\sqrt{7}-\sqrt{2}}{5}$

Therefore,  $\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}=\frac{\sqrt{7}-\sqrt{2}}{5}$

Answer 2

Answer:

$\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}=\frac{\sqrt{7}-\sqrt{2}}{5}$

Step-by-step explanation:

Given : Expression $\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}$

To find : Simplify the expression?

Solution :

Expression $\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}$

Rationalize the denominator by multiplying denominator with opposite sign,

$=\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}\times\frac{9-2\sqrt{14}}{9-2\sqrt{14}}$

$=\frac{(\sqrt{7}+\sqrt{2})(9-2\sqrt{14})}{9^2-(2\sqrt{14})^2}$

$=\frac{\sqrt{7}(9-2\sqrt{14})+\sqrt{2}(9-2\sqrt{14})}{81-4\times14}$

$=\frac{9\sqrt{7}-14\sqrt{2}+9\sqrt{2}-4\sqrt{7}}{81-56}$

$=\frac{5\sqrt{7}-5\sqrt{2}}{25}$

$=\frac{\sqrt{7}-\sqrt{2}}{5}$

Therefore, $\frac{\sqrt{7}+\sqrt{2}}{9+2\sqrt{14}}=\frac{\sqrt{7}-\sqrt{2}}{5}$