Question

(√7+√6)/ (√7-√6) मे हर का परिमेयकरण कीजिए​

Answer 1

Hey friend,

Here is the answer you were looking for:

$\frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} + \sqrt{6} }$

on rationalizing, we get

$\frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \times \frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} - \sqrt{6} }$

Using identities,

$\begin{gathered} {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \end{gathered}$

we get,

$\begin{gathered} \frac{ {( \sqrt{7}) }^{2} + {( \sqrt{6} )}^{2} + 2 \times \sqrt{7} \times \sqrt{6} }{ {( \sqrt{7} )}^{2} - {( \sqrt{6}) }^{2} } \\ \\ = \frac{7 + 6 + 2 \sqrt{42} }{7 - 6} \\ \\ = 13 + 2 \sqrt{42} \end{gathered}$

Hope this helps!!