Question

please answer it by today and I will mark as brainliest
question no.8
please​

Answer 1

Step-by-step explanation:

$7.) \: \: \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = a + b \sqrt{6} \\ = > \frac{ ({ \sqrt{3} - \sqrt{2} \: ) }^{2} }{ ({ \sqrt{3} })^{2} - ( { \sqrt{2} )}^{2} } = a + b \sqrt{6 } \\ = > \frac{ {( \sqrt{3} \: )}^{2} + ( { \sqrt{2} \: )}^{2} - 2. \sqrt{3} . \sqrt{2} }{3 - 2} = a + b \sqrt{6} \\ = > \frac{3 + 2 - 2 \sqrt{6} }{1} = a + b \sqrt{6} \\ = > 5 - 2 \sqrt{6} = a + b \sqrt{6} \\ now \: comparing \\ a = 5 \: \: and \: \: b \sqrt{6} = - 2 \sqrt{6} \\ b = - 2$

$9.)( \sqrt{5} + \sqrt{3} )(3 - \sqrt{2} \:) \\ = \sqrt{5} (3 - \sqrt{2} \: ) + \sqrt{3} (3 - \sqrt{2}) \\ = 5 \sqrt{3} - \sqrt{5} . \sqrt{2} + 3 \sqrt{3} - \sqrt{3} . \sqrt{2} \\ = 5 \sqrt{3} - \sqrt{10} + 3 \sqrt{3} - \sqrt{6}$

$\sqrt{48} - \sqrt{75} + \sqrt{90} - \sqrt{40} \\ = 4 \sqrt{3} - 5 \sqrt{3} + 3 \sqrt{10} - 2\sqrt{10} \\ = - \sqrt{3} + \sqrt{10} \\ = \sqrt{10} - \sqrt{3}$