Simplify the radical.
$\sqrt{75}$

• A. $3\sqrt5$
• B. $3\sqrt{25}$
• C. $5\sqrt3$
• D. $25\sqrt3$

Answer: (C)

Verified step by step guidance

1. Identify the expression to simplify: \( 75\sqrt{75} \).
2. Factor the number under the square root to find perfect squares: \( 75 = 25 \times 3 \).
3. Rewrite the expression using the factorization: \( 75\sqrt{75} = 75\sqrt{25 \times 3} \).
4. Apply the property of square roots: \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). This gives \( 75\sqrt{25} \times \sqrt{3} \).
5. Simplify \( \sqrt{25} \) to 5, resulting in \( 75 \times 5 \times \sqrt{3} \).