Use the product rule to rewrite the term inside the radical as a product, then simplify.
$-\sqrt{72x^2}$

• A. $6\sqrt2$ •$x$
• B. $-6x^2$
• C. $-6x$
• D. $-6\sqrt2$•$x$

Answer: (D)

Verified step by step guidance

1. Start with the expression inside the radical: \(\sqrt{72x^2}\). Use the product rule for radicals, which states that \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\), to rewrite this as \(\sqrt{72} \cdot \sqrt{x^2}\).
2. Simplify \(\sqrt{x^2}\). Since the square root and the square are inverse operations, \(\sqrt{x^2} = |x|\). For simplicity in algebraic expressions, this is often written as \(x\) assuming \(x\) is nonnegative.
3. Next, simplify \(\sqrt{72}\). Factor 72 into its prime factors or perfect squares: \$72 = 36 \times 2\(. Then apply the product rule again: \)\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2}$.
4. Since \(\sqrt{36} = 6\), rewrite \(\sqrt{72}\) as \$6\sqrt{2}\(. Now the expression inside the radical becomes \)6\sqrt{2} \cdot x$.
5. Don't forget the negative sign outside the radical in the original expression. So, the entire expression simplifies to \(-6x\sqrt{2}\).