Question

rationalize the denominator √3+√2/5+√2​

Answer 1

Step-by-step explanation:

√3+√2

5+√2

rationalizing number= 5-√2

now do it yourself

Answer 2

Given:-

Rationalize the denominator √3+√2/5+√2.

Solution:-

We know that,

$\frac{ \sqrt{3} + \sqrt{2} }{5 + \sqrt{2} } \\ \\ \frac{ \sqrt{3} + \sqrt{2} }{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} } \\ \\ \frac{ \sqrt{3}(5 - \sqrt{2}) + \sqrt{2}(5 - \sqrt{2}) }{ {(5)}^{2} \: - ( { \sqrt{2} }^{2}) } \\ \\ \frac{5 \sqrt{3} - \sqrt{6} +5 \sqrt{2} - 2 }{5 - 2} \\ \\ \frac{5 \sqrt{3} - \sqrt{6} + 5 \sqrt{2} - 2 }{3}$

Therefore,The answer is

$\boxed{ \frac{5 \sqrt{3} - \sqrt{6} + 5 \sqrt{2} - 2 }{3}}$