Question

Rationalise
$\frac{4\sqrt{3}+5\sqrt{2} }{\sqrt{48} +\sqrt{18} }$

Answer 1

Step-by-step explanation:

Solution :

$\: \: \: \: \: \: \: \: \: \frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} }$

$= > \frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \times \frac{ \sqrt{48} - \sqrt{18} }{ \sqrt{48} - \sqrt{18} }$

$= > \frac{(4 \sqrt{3} + 5 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} )}{( \sqrt{48} ) ^{2} - ( \sqrt{18}) ^{2} }$

$= > \frac{16 \times 3 - 12 \sqrt{6} + 20 \sqrt{6} - 15 \times 2 }{48 - 18}$

$= > \frac{18 + 8 \sqrt{6} }{30}$

$= > \frac{9 + 4 \sqrt{6} }{15} .$