Question

31. Rationalize (a)
1/√7+√2 (b) 1/√7​

Answer 1

Step-by-step explanation:

$\frac{1}{ \sqrt{7} + \sqrt{2} } \\ = \frac{ \sqrt{7} - \sqrt{2} }{( \sqrt{7} + \sqrt{2})( \sqrt{7} - \sqrt{2}) } \\ = \frac{ \sqrt{7} - \sqrt{2} }{ { \sqrt{7} }^{2} - { \sqrt{2} }^{2} } \\ = \frac{ \sqrt{7} - \sqrt{2} }{7 - 2} \\ = \frac{ \sqrt{7} - \sqrt{2} }{5}$

$\frac{1}{ \sqrt{7} } = \frac{ \sqrt{7} }{ \sqrt{7} \times \sqrt{7} } = \frac{ \sqrt{7} }{7}$