Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }$
A) $12 \sqrt { x }$
B) $14 \sqrt { 3 x }$
C) $17 \sqrt { x }$
D) $19 x$

Question

Quizplus · Accepted Answer

Using the distributive property, we can simplify this expression as follows:

$- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x } = -8 \cdot 2 \sqrt{x} + 2 \cdot 4 \sqrt{x} + 5 \cdot 5 \sqrt{x} = -16\sqrt{x} + 8\sqrt{x} + 25\sqrt{x} = 17\sqrt{x}$

Therefore, the best choice is C.

Use the Distributive Property to Help Simplify the Following Expression −84x+216x+525x- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }−84x​+216x​+525x​

Use the Distributive Property to Help Simplify the Following Expression $- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }$