Question

which expression is equivalent to $8\sqrt{108}$? a $15\sqrt{6}$ b $18\sqrt{6}$ c $48\sqrt{3}$ d $54\sqrt{3}$

Explanation:

Step1: Factor 108 into perfect square

$108 = 36 \times 3$

Step2: Split the square root

$8\sqrt{108} = 8\sqrt{36 \times 3} = 8 \times \sqrt{36} \times \sqrt{3}$

Step3: Simplify $\sqrt{36}$

$\sqrt{36} = 6$, so $8 \times 6 \times \sqrt{3}$

Step4: Calculate 8×6

$8 \times 6 = 48$

Answer:

C. $48\sqrt{3}$