Question

Rationalize -
1 /√5 +√3​

Answer 1

1/√5+√3 = (1)(√5-√3)/(√5+√3)(√5-√3).

Using identity (a+b)(a-b) = a^2 - b^2 :

= (√5-√3)/(5-3).

= (√5-√3)/2.

Ans: (√5-√3)/2.

Answer 2

Step-by-step explanation:

$\tt \hookrightarrow \frac{1}{ \sqrt{5} + \sqrt{3} } \\ \\ \tt \hookrightarrow \frac{1( \sqrt{5} - \sqrt{3}) }{( \sqrt{5} + \sqrt{3} )( \sqrt{5} - \sqrt{3} ) } \\ \\ \tt \hookrightarrow \frac{ \sqrt{5} - \sqrt{3} }{( \sqrt{5} ) {}^{2} - ( \sqrt{3} ) {}^{2} } \\ \\ \tt \hookrightarrow \frac{ (\sqrt{5} - \sqrt{3} )}{5 - 3} \\ \\ \tt \hookrightarrow \frac{ (\sqrt{5} - \sqrt{3} )}{2} \\ \\ \therefore \tt \: rationalised \: denominator \: is \: \frac{ (\sqrt{5} - \sqrt{3} ) }{2} .$