Question

2.rationalise the denom.​

Answer 1

Question :-

Rationalise denomination .

$\implies \: \frac{5 + \sqrt{2} }{3 - \sqrt{2} } \: \sf \frac{numenator}{denomenator}$

Answer :-

$\rightarrow \: \frac{17 + 8 \sqrt{2} }{7} \:$

Formula used :-

→ a² - b² =( a - b)(a + b)

Explanation :-

We have ,

$\rightarrow \: \frac{5 + \sqrt{2} }{3 - \sqrt{2} } \\ \\ \rightarrow \: \frac{5 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ \\ \rightarrow \: \frac{(5 + \sqrt{2})(3 + \sqrt{2} )}{ {3}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \rightarrow \: \frac{15 + 5 \sqrt{2} + 3 \sqrt{2} + 2 }{9 - 2} \\ \\ \rightarrow \: \frac{17 + 8 \sqrt{2} }{7}$