Question

rationalise the denominator of the following: root 5 - 2/root 5 plus 2

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{5 - 2} }{ \sqrt{5 + 2} } \\ = \frac{ \sqrt{5 - 2} }{ \sqrt{5 + 2} } \times \frac{ \sqrt{5 - 2} }{ \sqrt{5 - 2} } \\ (a +b {)}^{2} = {a}^{2} + {b}^{2} + 2ab) \\ = \frac{ { \sqrt{5} }^{2} + {2}^{2} - 2 \times \sqrt{5 \times 2} }{ { \sqrt{5} }^{2} - { 2} }^{2} } \\ = \frac{5 + 4 - 4 \sqrt{5} }{5 - 4} \\ = 9 - 4 \sqrt{5}$