Use the Product Rule to Simplify Square Roots
-$\sqrt { 448 \mathrm { x } ^ { 2 } }$
A) $8 | x | \sqrt { 7 }$
B) $8 \sqrt { 7 x ^ { 2 } }$
C) $8 x ^ { 2 } \sqrt { 7 }$
D) $8 \sqrt { 7 }$

Question

Quizplus · Accepted Answer

The Product Rule for square roots states that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$. First, factor 448 into $64 \times 7$ and $x^2$ into $x \cdot x$. Since $64$ is a perfect square, it simplifies to $8$, and $x^2$ simplifies to $|x|$ because the square root of any variable squared is the absolute value of that variable. Thus, $\sqrt{448x^2} = \sqrt{64 \cdot 7 \cdot x^2} = 8|x|\sqrt{7}$.

Use the Product Rule to Simplify Square Roots - 448x2\sqrt { 448 \mathrm { x } ^ { 2 } }448x2​

Use the Product Rule to Simplify Square Roots
- $\sqrt { 448 \mathrm { x } ^ { 2 } }$