Question

exercises simplify the quotient. 39. \\(\frac{2\sqrt{3}}{\sqrt{6}}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{6}$:
$\frac{2\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{2\sqrt{3 \times 6}}{\sqrt{6 \times 6}}$

Step2: Simplify radicals and denominator

Calculate products inside radicals and denominator:
$\frac{2\sqrt{18}}{6} = \frac{2 \times 3\sqrt{2}}{6}$

Step3: Simplify the expression

Reduce the numerical fraction:
$\frac{6\sqrt{2}}{6} = \sqrt{2}$

Answer:

$\sqrt{2}$