Question

simplify, rationalize the denomintaor of the following

Answer 1

Answer:

$1) \: \: \: {( \sqrt{7} - \sqrt{2}) }^{2} \\ = { \sqrt{7} }^{2} + { \sqrt{2} }^{2} - 2 \sqrt{7} \sqrt{2} \\ = 7 + 2 - 2 \sqrt{14} \\ = 9 - 2 \sqrt{14} \\ 2) \: \: \: \: ( \sqrt{2} + 1)( \sqrt{2} - 1) \\ = { \sqrt{2} }^{2} - {1}^{2} \\ = 2 - 1 \\ = 1$

rationalise

$\frac{1}{ \sqrt{5} } = \frac{1}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } \\ = \frac{ \sqrt{5} }{ { \sqrt{5} }^{2} } \\ = \frac{ \sqrt{5} }{5}$