Question

Simplify (4*root3 + 5*root2)/(root48 + root18

Answer 1

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→ Answer :

$\frac{9+4\sqrt{6} }{15}$

→ Step-by-step explanation :

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

→ Rationalize the denominator.

$=>\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}*\frac{4\sqrt{3}-3\sqrt{2}}{4\sqrt{3}-3\sqrt{2}} \\\\=>\frac{48-12\sqrt{6}+20\sqrt{6}-30 }{48-18}\\\\ =>\frac{18+8\sqrt{6} }{30}\\\\ =>\frac{9+4\sqrt{6} }{15}$

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