Question

Rationalise the denominator

Answer 1

Step-by-step explanation:

the answers are

1.√45/3

2.-(3√4+√6/15)

Answer 2

★$\bf{\underline{Answer::}}$

(i) $\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{5}-\sqrt{2}}$

$\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{5}-\sqrt{2}} \times \dfrac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}$

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

$\dfrac{(\sqrt{10}+4)+(\sqrt{15}+\sqrt{6})}{5-2}$

$\dfrac{\sqrt{10}+4+\sqrt{15}+\sqrt{6}}{3}$

(ii) $\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{3}- 3 \sqrt{2}}$

$\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{3}- 3 \sqrt{2}} \times \dfrac{\sqrt{3}+ 3 \sqrt{2}}{\sqrt{3}+ 3 \sqrt{2}}$

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

$\dfrac{(\sqrt{15}+ 3 \sqrt{10})-(3+ 3 \sqrt{6})}{3- 18}$

$\dfrac{(\sqrt{15}+ 3 \sqrt{10})-(3+ 3 \sqrt{6})}{-15}$