Use the Product Rule to Simplify Square Roots
-$\sqrt { 7 x ^ { 2 } } \cdot \sqrt { 21 x }$
A) $7 | x | \sqrt { 3 x }$
B) $7 | x | \sqrt { 3 }$
C) $7 x ^ { 2 } \sqrt { 3 x }$
D) $7 | x | \sqrt { 3 x ^ { 2 } }$

Question

Quizplus · Accepted Answer

The product rule for square roots states that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$. Applying this rule, we get $\sqrt{7x^2} \cdot \sqrt{21x} = \sqrt{7x^2 \cdot 21x} = \sqrt{147x^3}$. Simplifying inside the square root gives $\sqrt{7 \cdot 21 \cdot x^3} = \sqrt{7 \cdot 3 \cdot 7 \cdot x^2 \cdot x} = 7|x| \sqrt{3x}$, since $\sqrt{x^2} = |x|$ to account for both positive and negative values of $x$.

Use the Product Rule to Simplify Square Roots - 7x2⋅21x\sqrt { 7 x ^ { 2 } } \cdot \sqrt { 21 x }7x2​⋅21x​

Use the Product Rule to Simplify Square Roots
- $\sqrt { 7 x ^ { 2 } } \cdot \sqrt { 21 x }$