$$ 2 \times 2 \times 3 \times 5$$

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$\int \frac{1}{2 + 3 s i n x} d x$

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Evaluate

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

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Simplify:

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

(ii) $\frac{1}{2 + \sqrt{3}} + \frac{2}{\sqrt{5} - \sqrt{3}} + \frac{1}{2 - \sqrt{5}}$

(iii) $\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} - \frac{3}{\sqrt{5} + \sqrt{2}}$

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2. Write in exponential form.

a) 5 × 5 × 5 × 5 × 5 = ____________

b) (4) × (4) × (4) = ____________

c) 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = ____________

d) (8) × (8) × (8) × (8) = ____________

e) 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = __

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Find the value of given expression

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

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