Question

rationalize this question​

Answer 1

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

Answer 2

TO RATIONALISE THE DENIMINATOR

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

ANSWER

$\frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} - \sqrt{6} } \\ \\ \\ \\ = \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} - \sqrt{6} } \times 1 \\ \\ \\ \\ = \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \\ \\ \\ \\ = \frac{{( \sqrt{7} + \sqrt{6}) }^{2}}{ { \sqrt{7} }^{2} - { \sqrt{6} }^{2} } \\ \\ \\ \\ = \frac{7 + 2 \sqrt{7 } \sqrt{6} + 6 }{7 - 6} \\ \\ \\ \\ = \boxed{ \boxed{13 + 2 \sqrt{42} }}$

We have to keep in mind the following things at the time of rationalisation :-

》We should try to convert the denominator to numerator. If there is any one square root term then we can multiply the same number both in numerator and denominator

》If we have two sq.root terms in denominator when we should interchange the middle symbol and multiply the respective factor both in numerator and denominator so as to apply a^2 - b^2 identity.

》IDENTITIES

(a + b)^2 = a^2 + b^2 + 2ab

(a - b)^2 = a^2 + b^2 - 2ab

(a + b)(a - b) = a^2 - b^2