Question

Rationalise (7+3√2)/(7-3√2) and add it to √7-√2.

Answer 1

Answer:

7²-(3√2)²

= 49. - 18

31 and then add √7-√2

Answer 2

Step-by-step explanation:

$\blue{= \frac{(7 + 3 \sqrt{2}) }{(7 - 3 \sqrt{2})}} \\ \blue{ = \frac{(7 + 3 \sqrt{2})}{(7 - 3 \sqrt{2})} \times \frac{(7 + 3 \sqrt{2})}{(7 + 3 \sqrt{2})}} \\ \blue{= \frac{(7 + 3 \sqrt{2}) \times (7 + 3 \sqrt{2})}{ {7}^{2} - (3 \sqrt{2})^{2} }} \: \: \: \: \bold\pink{\mathtt{(using \:( a - b)(a + b))}} \\ \blue{ = \frac{7(7 + 3 \sqrt{2}) + 3 \sqrt{2}(7 + 3 \sqrt{2}) }{49 - 9 \times 2}} \\ \blue{= \frac{49 + 21 \sqrt{2} + 21 \sqrt{2} + 3 \times 3 \times 2}{49 - 18}} \\ \blue{= \frac{49 + 18 + 42 \sqrt{2} }{31}} \\ \blue{= \frac{67 + 42 \sqrt{2} }{31}} \\ \\ \\ \\ \\ \bold{Now, \: we \: add \: \sqrt{7} - \sqrt{2}} \\ \\ \frac{67 + 42 \sqrt{2} }{31} + \sqrt{7} - \sqrt{2} = \frac{67 + 42 \sqrt{2} + 31 \sqrt{7} - 31 \sqrt{2} }{31} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{\boxed{ = \frac{67 + 11 \sqrt{2 } + 31 \sqrt{7} }{31}}}$

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