Question

exercises simplify the quotient. 40. \\(\frac{2\sqrt{3}}{\sqrt{5}}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{5}$:
$\frac{2\sqrt{3}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{2\sqrt{3} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}}$

Step2: Simplify the expressions

Use $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ and $\sqrt{a} \times \sqrt{a} = a$:
$\frac{2\sqrt{15}}{5}$

Answer:

$\frac{2\sqrt{15}}{5}$