Question

rationalise the denominator 3/√3+√5-√2

Answer 1

Answer:

The simplified form is $\frac{\sqrt{3}}{2}-\frac{3\sqrt{2}}{4}+\frac{\sqrt{30}}{4}$.

Step-by-step explanation:

The given expression is

$\frac{3}{\sqrt{3}+\sqrt{5}-\sqrt{2}}$

Rationalize the denominator.

$\frac{3}{(\sqrt{3}+\sqrt{5})-\sqrt{2}}\times \frac{(\sqrt{3}+\sqrt{5})+\sqrt{2}}{(\sqrt{3}+\sqrt{5})+\sqrt{2}}$

$\frac{3(\sqrt{3}+\sqrt{5})+3\sqrt{2}}{(\sqrt{3}+\sqrt{5})^2-(\sqrt{2})^2}$

$\frac{3\sqrt{3}+3\sqrt{5}+3\sqrt{2}}{3+5+2\sqrt{15}-2}$

$\frac{3\sqrt{3}+3\sqrt{5}+3\sqrt{2}}{6+2\sqrt{15}}$

Rationalize the denominator.

$\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})}{6+2\sqrt{15}}\times \frac{6-2\sqrt{15}}{6-2\sqrt{15}}$

$\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{6^2-(2\sqrt{15})^2}$

$\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{36-60}$

$\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{-24}$

$-\frac{(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{8}$

$\frac{\sqrt{3}}{2}-\frac{3\sqrt{2}}{4}+\frac{\sqrt{30}}{4}$

Therefore the simplified form is $\frac{\sqrt{3}}{2}-\frac{3\sqrt{2}}{4}+\frac{\sqrt{30}}{4}$.

Answer 2

Step-by-step explanation:

thankyou

myself

Ashakiran from class 9