Question

1. simplify the expression below.

\sqrt{\frac{5x}{12}}
a. \frac{\sqrt{5x}}{6}
c. 4\sqrt{15x}
b. \frac{\sqrt{15x}}{6}
d. \frac{\sqrt{15x}}{3}

Explanation:

Step1: Split root into fraction

$\sqrt{\frac{5x}{12}} = \frac{\sqrt{5x}}{\sqrt{12}}$

Step2: Rationalize the denominator

Multiply numerator/denominator by $\sqrt{3}$:
$\frac{\sqrt{5x} \cdot \sqrt{3}}{\sqrt{12} \cdot \sqrt{3}} = \frac{\sqrt{15x}}{\sqrt{36}}$

Step3: Simplify the denominator

$\sqrt{36} = 6$, so:
$\frac{\sqrt{15x}}{6}$

Answer:

B. $\frac{\sqrt{15x}}{6}$