Question

rationalize the denominator of 1+ root 6 / 7 + root 2​

Answer 1

Given :-

• $\tt \: \frac{1 + \sqrt{6} }{7 + \sqrt{2} }$

To Find :-

• Rationalize the denominator.

Solution :-

$\mapsto \: \tt \: \frac{1 + \sqrt{6} }{7 + \sqrt{2} }$

$\mapsto \tt \: \frac{1 + \sqrt{6} }{7 + \sqrt{2} } \times \frac{7 - \sqrt{2} }{7 - \sqrt{2} }$

$\mapsto \tt \: \frac{(1 + \sqrt{6} ) \times (7 - \sqrt{2} )}{(7 - \sqrt{2} ) \times (7 - \sqrt{2}) }$

$\mapsto \tt \: \frac{1(7 - \sqrt{2} ) + \sqrt{6}(7 - \sqrt{2} ) }{(7 + \sqrt{2}) \times (7 - \sqrt{2} ) }$

$\mapsto \tt \: \frac{7 - \sqrt{2} + 7 \sqrt{6} - \sqrt{12} }{49 - 2}$

$\mapsto \tt \: \boxed{ \red{\frac{7 - \sqrt{2} + 7 \sqrt{ 6 } - \sqrt{12} }{47} }}$

Formulae Used :-

• (a + b) (a - b) = a² - b²