Question

1. simplify the expression below.

\\(\frac{12\sqrt{3}}{\sqrt{8}}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{8}$:
$\frac{12\sqrt{3}}{\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}} = \frac{12\sqrt{3 \times 8}}{8}$

Step2: Simplify the product inside root

Calculate $3 \times 8 = 24$, then simplify $\sqrt{24}$:
$\frac{12\sqrt{4 \times 6}}{8} = \frac{12 \times 2\sqrt{6}}{8}$

Step3: Simplify the numerical terms

Multiply and reduce the fraction:
$\frac{24\sqrt{6}}{8} = 3\sqrt{6}$

Answer:

$3\sqrt{6}$