Simplify the expression. Assume all variables represent positive real numbers.
-$6 \sqrt { 32 x ^ { 2 } } - 3 \sqrt { 18 x ^ { 2 } } - \sqrt { 2 x ^ { 2 } }$
A) $2 x \sqrt { 14 }$
B) $14 x \sqrt { 2 }$
C) $3 x \sqrt { 14 }$
D) $15 x \sqrt { 2 }$

Question

Quizplus · Accepted Answer

First, simplify each term inside the square roots: $6\sqrt{32x^2} = 6\sqrt{16 \cdot 2x^2} = 6 \cdot 4x\sqrt{2} = 24x\sqrt{2}$, $3\sqrt{18x^2} = 3\sqrt{9 \cdot 2x^2} = 3 \cdot 3x\sqrt{2} = 9x\sqrt{2}$, and $\sqrt{2x^2} = x\sqrt{2}$. Combining these gives $24x\sqrt{2} - 9x\sqrt{2} - x\sqrt{2} = 14x\sqrt{2}$.

Simplify the Expression 632x2−318x2−2x26 \sqrt { 32 x ^ { 2 } } - 3 \sqrt { 18 x ^ { 2 } } - \sqrt { 2 x ^ { 2 } }632x2​−318x2​−2x2​

Simplify the Expression $6 \sqrt { 32 x ^ { 2 } } - 3 \sqrt { 18 x ^ { 2 } } - \sqrt { 2 x ^ { 2 } }$