Question

plz don't spam
all three​

Answer 1

Answer:

i) - √3 - √5

ii) 5 + 2√6

iii) 2√5 - 2√2

Step-by-step explanation:

Rationalizing: Rationalizing is nothing but multiply the denominator by the conjugate surd or rationalizing factors to make the rational term from the irrational term.

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

$ii) \frac{ (\sqrt{3} + \sqrt{2} )( \sqrt{3} + \sqrt{2} ) }{( \sqrt{3} - \sqrt{2}) ( \sqrt{3} + \sqrt{2} ) } \\ \\ \frac{ {( \sqrt{3}) }^{2} + {( \sqrt{2} )}^{2} + 2 \sqrt{3} . \sqrt{2} }{ { (\sqrt{3} )}^{2} - {( \sqrt{2}) }^{2} } \\ \\ \frac{3 + 2 + 2 \sqrt{6} }{3 - 2} \\ \\ \frac{5 + 2 \sqrt{6} }{1} \\ \\ \bold{ 5 + 2 \sqrt{6} }$

$iii) \frac{6}{ \sqrt{5} + \sqrt{2} } \\ \\ \frac{6( \sqrt{5} - \sqrt{2} ) }{( \sqrt{5} + \sqrt{2} )( \sqrt{5} - \sqrt{2} )} \\ \\ \frac{6( \sqrt{5} - \sqrt{2} ) }{ { (\sqrt{5} )}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \frac{6( \sqrt{5} - \sqrt{2} )}{5 - 2} \\ \\ \frac{6( \sqrt{5 } - \sqrt{2} )}{3} \\ \\ 2( \sqrt{5} - \sqrt{2} ) \\ \\ \bold{2 \sqrt{5} - 2 \sqrt{2}}$