Perform the indicated operations. Assume that all variables represent positive numbers.
-$\sqrt { 12 x ^ { 3 } } - 8 \sqrt { 108 x ^ { 3 } }$
A) $- 8 \sqrt { - 96 x ^ { 3 } }$
B) $- 46 x \sqrt { 3 x }$
C) $50 x \sqrt { 3 x }$
D) $- 46 \sqrt { 3 x ^ { 3 } }$

Question

Quizplus · Accepted Answer

First, simplify each term under the square root and factor out perfect squares: $\sqrt{12x^3} = \sqrt{4 \cdot 3 \cdot x^2 \cdot x} = 2x\sqrt{3x}$ and $8\sqrt{108x^3} = 8\sqrt{36 \cdot 3 \cdot x^2 \cdot x} = 24x\sqrt{3x}$. Subtracting the second expression from the first gives $2x\sqrt{3x} - 24x\sqrt{3x} = -22x\sqrt{3x}$, which is not listed as an option due to a mistake in my calculation. Correcting the calculation: $8\sqrt{108x^3} = 8\sqrt{36 \cdot 3 \cdot x^2 \cdot x} = 48x\sqrt{3x}$, so the correct subtraction is $2x\sqrt{3x} - 48x\sqrt{3x} = -46x\sqrt{3x}$, which matches option B.

Perform the Indicated Operations 12x3−8108x3\sqrt { 12 x ^ { 3 } } - 8 \sqrt { 108 x ^ { 3 } }12x3​−8108x3​

Perform the Indicated Operations $\sqrt { 12 x ^ { 3 } } - 8 \sqrt { 108 x ^ { 3 } }$