Question

rationalise the denominator and simplify √48+√32/√27-√18

Answer 1

Answer:

The rationalization of the denominator is $\frac{(20+8\sqrt{6})}{3}$.

Step-by-step explanation:

Consider the provided expression.

$\frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}-\sqrt{18}}}$

Rationalize the denominator by multiplying √27+√18 with numerator and denominator.

$\frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}-\sqrt{18}}}\times \frac{\sqrt{27}+\sqrt{18}}{\sqrt{27}+\sqrt{18}}$

$\frac{(\sqrt{48}+\sqrt{32})\times(\sqrt{27}+\sqrt{18})}{27-18}}$

$\frac{(4\sqrt{3}{+4\sqrt{2})}\times(3\sqrt{3}+3\sqrt{2})}{9}}$

$\frac{(4\sqrt{3}{+4\sqrt{2})}\times(\sqrt{3}+\sqrt{2})}{3}}$

$\frac{(12+4\sqrt{6}+4\sqrt{6}+8)}{3}$

$\frac{(20+8\sqrt{6})}{3}$

Hence, the rationalization of the denominator is $\frac{(20+8\sqrt{6})}{3}$.