Question

rationalise the denominator please be fast​

Answer 1

Answer:

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

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

$\frac{ \sqrt{5} + \sqrt{2} - \sqrt{3} }{4 + 2 \sqrt{3} }$

$\frac{ \sqrt{5} + \sqrt{2} - \sqrt{3} }{4 + 2 \sqrt{3} } \times \frac{4 - 2 \sqrt{3} }{4 - 2 \sqrt{3} }$

$\frac{( \sqrt{5} + \sqrt{2} - \sqrt{3})(4 + 2 \sqrt{3} )}{16 - 12}$

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

$= \frac{( \sqrt{5} + \sqrt{2} - \sqrt{3}) ( 2 + \sqrt{3} )}{2}$