Question

rationalise the denominator and simplify under root 7 + under root 2 by 9 + 2 under root 14

Answer 1

Hello Mate!

$\frac{ \sqrt{7} + \sqrt{2} }{9 + 2 \sqrt{14} } \\ \\ rationalize \\ \\ \frac{ \sqrt{7} + \sqrt{2} }{9 + 2 \sqrt{14} } \times \frac{9 - 2 \sqrt{14} }{9 - 2 \sqrt{14} } \\ \frac{9 \sqrt{7} - 2 \sqrt{98} + 9 \sqrt{2} - 2 \sqrt{28} }{81 - 56} \\ \sqrt{98 } = \sqrt{2 \times 7 \times 7} = 7 \sqrt{2} \\ \sqrt{28} = \sqrt{2 \times 2 \times 7} = 2 \sqrt{7} \\ \frac{9 \sqrt{7} - 14 \sqrt{2} + 9 \sqrt{2} - 4 \sqrt{7} }{25} \\ \frac{5 \sqrt{7} - 5 \sqrt{2} }{25} = \frac{5 \sqrt{7} }{25} - \frac{5 \sqrt{2} }{25} \\ \frac{ \sqrt{7} - \sqrt{2} }{5}$

Hope it helps☺!

Answer 2

Answer:

$\text{The rationalization is }\frac{\sqrt7-\sqrt2}{5}$

Step-by-step explanation:

We have to rationalize the given expression

$\frac{\sqrt7+\sqrt2}{9+2\sqrt{14}}$

Expression: $\frac{\sqrt7+\sqrt2}{9+2\sqrt{14}}$

Rationalizing, we get

$\frac{\sqrt7+\sqrt2}{9+2\sqrt{14}}\times \frac{9-2\sqrt{14}}{9-2\sqrt{14}}$

$=\frac{(\sqrt7+\sqrt2)(9-2\sqrt{14})}{(9+2\sqrt{14})(9-2\sqrt{14})}$

$=\frac{9\sqrt7-2\sqrt{98}+9\sqrt2-2\sqrt{28}}{(9^2-(2\sqrt{14})^2}$

$=\frac{9\sqrt7-14\sqrt{2}+9\sqrt2-4\sqrt{7}}{81-56}$

$=\frac{5\sqrt7-5sqrt2}{25}$

$=\frac{\sqrt7-\sqrt2}{5}$

which is required simplification.