Simplify the following.
$\sqrt{49m^2}$

• A. $49m$
• B. $7$
• C. $7m$
• D. $7m^2$

Answer: (C)

Verified step by step guidance

1. Identify the expression to simplify: \(\sqrt{49m^2}\).
2. Recall that the square root of a product is the product of the square roots, so rewrite as \(\sqrt{49} \times \sqrt{m^2}\).
3. Simplify \(\sqrt{49}\) by recognizing that 49 is a perfect square, so \(\sqrt{49} = 7\).
4. Simplify \(\sqrt{m^2}\) by using the property \(\sqrt{x^2} = |x|\), so \(\sqrt{m^2} = |m|\).
5. Combine the simplified parts to get \$7|m|$. If $m$ is known to be nonnegative, this simplifies further to \$7m$.