Question

simplify 5+2 root 3/7+4 root 3

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

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

First rationalise the denominator.

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} }$


$= \frac{(5 + 2 \sqrt{3})(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3})(7 - 4 \sqrt{3} )}$


USING IDENTITY : a² - b² = ( a - b ) ( a + b )


$= \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{ {(7)}^{2} - {(4 \sqrt{3)} }^{2} }$


$= \frac{11 - 6 \sqrt{3} }{49 - 48}$

$= \frac{11 - 6 \sqrt{3} }{1}$


$= 11 - 6 \sqrt{3}$

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HOPE IT HELPS YOU..

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