Simplify the radical.
$\(\sqrt{63x^2}\)$

• A. $63\(\sqrt{x}\)$
• B. $3\(\sqrt{7x}\)$
• C. $x\(\sqrt{63}\)$
• D. $3x\(\sqrt\)7$

Answer: (D)

Verified step by step guidance

1. Identify the expression under the radical: \( \sqrt{63x^2} \).
2. Break down the expression under the radical into its prime factors: \( 63 = 3^2 \times 7 \) and \( x^2 \).
3. Apply the property of square roots: \( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \). This gives us \( \sqrt{3^2 \times 7 \times x^2} = \sqrt{3^2} \cdot \sqrt{7} \cdot \sqrt{x^2} \).
4. Simplify each part: \( \sqrt{3^2} = 3 \) and \( \sqrt{x^2} = x \). Therefore, the expression becomes \( 3x \cdot \sqrt{7} \).
5. Combine the simplified terms to get the final simplified expression: \( 3x \sqrt{7} \).