Question

Pls solve the Q7 with proper steps

Answer 1

$\sqrt{ \frac{5 + \sqrt{3} }{5 - \sqrt{3} } } \\ \\ = \sqrt{ \frac{5 + \sqrt{3} }{5 - \sqrt{3} } } \: \times \sqrt{ \frac{5 + \sqrt{3} }{5 + \sqrt{3} } } \\ \\ = \sqrt{ \frac{(5 + \sqrt{3} )(5 + \sqrt{3}) }{(5 - \sqrt{3} )(5 + \sqrt{3}) } } \\ \\ = \sqrt{ \frac{ {(5 + \sqrt{3}) }^{2} }{ {(5)}^{2} - {( \sqrt{3} )}^{2} } } \\ \\ = \frac{ \sqrt{ {(5 + \sqrt{3}) }^{2} } }{ \sqrt{25 - 3} } \\ \\ = \frac{5 + \sqrt{3} }{ \sqrt{22} }$

$= \frac{5 + \sqrt{3} }{ \sqrt{22} } \times \frac{ \sqrt{22} }{ \sqrt{22} } \\ \\ = \frac{(5 + \sqrt{3} ) \times \sqrt{22} }{22}$

$\sqrt{3} = 1.73 \\ \sqrt{22} = 4.69$

$\frac{(5 + \sqrt{3} ) \times \sqrt{22} }{22} \\ \\ = \frac{(5 + 1.73 ) \times 4.69}{22} \\ \\ = \frac{6.73 \times 4.69}{22} \\ \\ = 1.434\\ \\ \approx 1.43\ (upto\ three\ significant\ figures)$

Answer 2

$\huge{\bold{\sqrt{\frac{5+ \sqrt{3}}{5- \sqrt{3}}}}}$

=$\huge{\bold{\sqrt{ \frac{5+\sqrt{3}}{5-\sqrt{3}}}\times\sqrt{\frac{5+\sqrt{3}}{5+\sqrt{3}}}}}}$

for more see the above attachment

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$\orange{\boxed{\blue{\boxed{\green{\bold{Please\: mark\: it\:as\: brainlist}}}}}}$