Question

if N=√9+√7 then 1/N=?​

Answer 1

N = √9 + √7

therefore 1/N = 1/(√9 + √7)

rationalizing it,

= 1/(√9 + √7) × (√9 - √7)/(√9 - √7)

= (√9 - √7)/(√9)²-(√7)²

= (√9 - √7)/(9 - 7)

= (√9 - √7)/2

Answer 2

Solution:-

$\bold{N = \sqrt{9} + \sqrt{7} }$

$\implies \bold{ \frac{ 1}{N} = \frac{1}{ \sqrt{9} + \sqrt{7} } }$

$\implies \bold{ \frac{ 1}{N} = \frac{1}{ \sqrt{9} + \sqrt{7} } \times \frac{ \sqrt{9} - \sqrt{7} }{ \sqrt{9 - \sqrt{7} } } }$

$\implies \bold{ \frac{ 1}{N} = \frac{\sqrt{9 }- {\sqrt{7} } }{(9 - 7) } }$

$\implies \bold{ \frac{ 1}{N} = \frac{\sqrt{9 }- {\sqrt{7} } }{(2) } }$