Question

Simplify the following by rationalizing the denominator :

7 root 3 - 5 root 2 / root 48 + root 18

Answer 1

$\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ = \frac{(7 \sqrt{3} - 5 \sqrt{2}) \times (4 \sqrt{3} - 3 \sqrt{2} )}{(4 \sqrt{3} + 3 \sqrt{2})(4 \sqrt{3} - 3 \sqrt{2} ) } \\ = \frac{28 \times 3 - 21 \sqrt{6} - 20 \sqrt{6} + 15 \times 2)}{48 - 18} \\ = \frac{84 + 30 - 41 \sqrt{6} }{30} \\ = \frac{114 - 41 \sqrt{6} }{30}$