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: \(\sqrt{72x^2}\). 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. Recognize that \(\sqrt{x^2}\) simplifies to \(|x|\), but since we usually assume \(x\) is nonnegative in algebra problems unless otherwise stated, this simplifies to \(x\).
3. Next, simplify \(\sqrt{72}\). Factor 72 into its prime factors or perfect squares: \(72 = 36 \times 2\), so \(\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2}\).
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 from the original expression. So, the entire expression simplifies to \(-6x\sqrt{2}\).