Question

$5 + 2 \sqrt{3 \div 7 + 4 \sqrt{3} }$
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Answer 1

Question:-

$find \: the \: value \: of \: \: \dfrac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} }$

Solution:-

$\dfrac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} }$

$take \: 2 \: common \: on \: numerator \: and \: denominator$

$= \dfrac{2(5 + \sqrt{3} )}{2(7 + 2 \sqrt{3} )}$

$= \dfrac{5 + \sqrt{3} }{7 + 2 \sqrt{3} }$

$again \: take \: \sqrt{3} as \: common \: on \: both \: numerator \: and \: denominator$

$= \dfrac{ \sqrt{3} (5 + 1)}{ \sqrt{3}(7 + 2) }$

$= \dfrac{5 + 1}{7 + 2}$

$= \dfrac{6}{9}$

$= \dfrac{2}{3}$

Answer:-

$\dfrac{2}{3}$