Question

Rationalise the denominator of
2 / √5+ √3+2

Answer 1

• $\sqrt{5 + \sqrt{3 + 2 \\ } }$
• $\sqrt{5 + \sqrt{5} }$
• root over and will cancel
• Answer:

so .. .1/10 where 10 is denominator

Answer 2

Answer:

$\frac{2}{ \sqrt{5} + \sqrt{3} + 2 } \\ = \frac{2}{( \sqrt{5}) + ( \sqrt{3} + 2) } \\ = \frac{2}{( \sqrt{5}) + ( \sqrt{3} + 2) } \times \frac{(\sqrt{5}) - ( \sqrt{3} + 2)}{( \sqrt{5}) - ( \sqrt{3} + 2) } \\ = \frac{2 \sqrt{5} - 2 \sqrt{3} - 4 }{ {( \sqrt{5}) }^{2} - {( \sqrt{3} + 2) }^{2} } \\ = \frac{2 \sqrt{5} - 2 \sqrt{3} - 4 }{5 - 3 - 4 - 4 \sqrt{3} } \\ = \frac{2( \sqrt{5} - \sqrt{3}) - 4 }{ - 2 - 4 \sqrt{3} } \\ = \frac{2( \sqrt{5} - \sqrt{3}) - 4 }{ - 2(1 + \sqrt{3}) } \\ = \frac{( \sqrt{3} - \sqrt{5}) + 2 }{1 + \sqrt{3} } \\ = \frac{( \sqrt{3} - \sqrt{5}) + 2 }{1 + \sqrt{3} }$

rest it is in simplified form and youcan solve it.

Hope it helps till here