Question

Simplify 14root 3+5root2/ root48 + root 18

Answer 1

$\textsf{\huge{\underline{ Hello Mate! }}}$

$\textsf{\red{So, on rationalizing we get}}$

$= > \frac{14 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ \\ = > \frac{14 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{ {2}^{4} \times 3} + \sqrt{ {3}^{2} \times 2} } \\ \\ = > \frac{14 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ \\ = > \frac{14 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ = > \frac{168 - 42 \sqrt{6} + 20 \sqrt{3} - 30 }{48 - 18} \\ \\ = > \frac{138 - 22 \sqrt{6} }{30} \\ \\ = > \frac{2(69 - 11 \sqrt{6}) }{2(15)} \\ \\ = > \frac{69 - 11 \sqrt{6} }{15}$

$\textbf{Have great future ahead!}$