Question

answer .................................​

Answer 1

Answer:

0.2134

11+2√30=21.95

1/√11+2√30=o.2134

Answer 2

Step by Step Solution

$\frac{1}{ \sqrt{11 + 2 \sqrt{30} } } \\ = \frac{1}{ \sqrt{( \sqrt{5} ) { }^{2} + 2. \sqrt{5}. \sqrt{6} + (\sqrt{6} ) {}^{2} } } \\ = \frac{1}{ \sqrt{( \sqrt{5} + \sqrt{6} ) {}^{2} } } \\ = \frac{1}{ \sqrt{6} + \sqrt{5} } \\ now \: doing \: rationalising \: of \: denominator \: we \: get \: \\ = \frac{1( \sqrt{6} - \sqrt{5} ) }{( \sqrt{6} + \sqrt{5} )( \sqrt{6} - \sqrt{5} )} \\ = \frac{ \sqrt{6} + \sqrt{5} }{6 - 5} \\ = \sqrt{6} - \sqrt{5}$