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

• A. $6\sqrt{2}$ •$x$
• B. $-6x^2$
• C. $-6x$
• D. $-6\sqrt{2}$•$x$

Answer: (D)

Verified step by step guidance

1. Start with the expression inside the radical: \(-\sqrt{72x^2}\). Recognize that the product rule for radicals states \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\), so rewrite the radicand as a product: \$72x^2 = 72 \cdot x^2$.
2. Apply the product rule to separate the radical: \(-\sqrt{72x^2} = -\sqrt{72} \cdot \sqrt{x^2}\).
3. Simplify \(\sqrt{x^2}\). Since \(x^2\) is a perfect square, \(\sqrt{x^2} = |x|\). Assuming \(x\) is nonnegative or considering the principal root, this simplifies to \(x\).
4. Next, simplify \(\sqrt{72}\). Factor 72 into its prime factors or perfect squares: \$72 = 36 \times 2\(, so \)\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}$.
5. Combine all parts: \(-\sqrt{72x^2} = - (6\sqrt{2}) \cdot x = -6\sqrt{2} \cdot x\). This is the simplified form using the product rule.