Question

SIMPLIFY BY RATIONALISING THE DENOMINATOR

Answer 1

Answer:

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Answer 2

Answer:

$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}$=6√2 - 2√6

Step-by-step explanation:

we have to simplify$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}$

we simplify by rationalizing the denominator of each term.

$\implies\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}\times\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}\times\frac{\sqrt{6}-\sqrt{3}}{\sqrt{6}-\sqrt{3}}$

$\implies\frac{4\sqrt{3}-6\sqrt{2}}{2-3}+\frac{12\sqrt{3}-6\sqrt{6}}{6-3}$

$\implies\frac{4\sqrt{3}-6\sqrt{2}}{-1}+\frac{12\sqrt{3}-6\sqrt{6}}{3}$

$\implies-4\sqrt{3}+6\sqrt{2}+4\sqrt{3}-2\sqrt{6}$

6√2 - 2√6

Therefore,$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}$=6√2 - 2√6