Question

amswer 8. & 9. all parts plzz ASAP

Answer 1

Hi...☺

Here is your answer...✌

$8. \: \: \: \: Simplify \: : \\ \\ (a). \: (4 + \sqrt{2} )(4 - \sqrt{2} ) \\ \\ = {4}^{2} - ( { \sqrt{2}) }^{2} \\ \\ = 16 - 2 \\ \\ = 14 \\ \\ (b). \: \: ( \sqrt{5} - \sqrt{2} )( \sqrt{2} - \sqrt{3} ) \\ \\ = \sqrt{5} \times \sqrt{2} - \sqrt{5} \times \sqrt{ 3} - \sqrt{2} \times \sqrt{2} + \sqrt{2} \times \sqrt{3} \\ \\ = \sqrt{10} - \sqrt{15} - 2 + \sqrt{6} \\ \\ (c). \: \:( 3 - \sqrt{3} ) {}^{2} \\ \\ = {3}^{2} + {( \sqrt{3})}^{2} + 2 \times 3 \times \sqrt{3} \\ \\ = 9 + 3 - 6 \sqrt{3 } \\ \\ = 12 - 6 \sqrt{3} \\ \\ (d). \: \: {( \sqrt{5} - \sqrt{3} )}^{2} \\ \\ = ( { \sqrt{5} )}^{2} + ( { \sqrt{3} )}^{2} - 2 \times \sqrt{5} \times \sqrt{3} \\ \\ = 5 + 3 - 2\sqrt{15} \\ \\ = 8 - 2\sqrt{15} \\ \\ (9). \: \: \: Rationalis e\: the \: denominator \\ \\ (a). \: \: \frac{ \sqrt{5} }{2 \sqrt{3} } = \frac{ \sqrt{5} \times \sqrt{3} }{2 \sqrt{3} \times \sqrt{3} } \\ \\ = \frac{ \sqrt{15} }{2 \times 3} = \frac{ \sqrt{15} }{6} \\ \\ (b). \: \: \: \frac{1 }{2 + \sqrt{3} } = \frac{1 \times( 2 - \sqrt{3}) }{(2 + \sqrt{3}) \times( 2 - \sqrt{3}) } \\ \\ = \frac{2 - \sqrt{3} }{ {2}^{2} - {( \sqrt{3} )}^{2} } = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ = 2 - \sqrt{3} \\ \\ (c). \: \: \frac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ = \frac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ = \frac{9 + 8 - 12 \sqrt{2} }{ {3}^{2} - {(2 \sqrt{2} )}^{2} } \\ \\ = \frac{17 - 12 \sqrt{2} }{9 - 8} \\ \\ = 17 - 12 \sqrt{2} \\ \\ (d). \: \: \frac{4}{ \sqrt{7} + \sqrt{3} } = \frac{4}{ \sqrt{7} + \sqrt{3} } \times \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} - \sqrt{3} } \\ \\ = \frac{4 ( \sqrt{7} - \sqrt{3} ) }{7 - 3} = \frac{4( \sqrt{7} - \sqrt{3} ) }{4} \\ \\ = \sqrt{7} - \sqrt{3} \\ \\ (e). \: \: \frac{1}{5 + 3 \sqrt{2} } = \frac{1}{5 + 3 \sqrt{2} } \times \frac{5 - 3 \sqrt{2} }{5 - 3 \sqrt{2} } \\ \\ = \frac{5 - 3 \sqrt{2} }{ {5}^{2} - ( {3 \sqrt{2} )}^{2} } \\ \\ = \frac{5 - 3\sqrt{2} }{25 - 18} \\ \\ = \frac{5 - 3 \sqrt{2} }{7}$

Answer 2

Hello Dear User !

Plz refer to the pic above

Hope it helps!☺