Simplify the given square root.
$\sqrt{-75}$

• A. $25i\sqrt3$
• B. $5i\sqrt3$
• C. $3i\sqrt5$
• D. $75i$

Answer: (B)

Verified step by step guidance

1. Recognize that the expression involves the square root of a negative number, \(\sqrt{-75}\). Recall that \(\sqrt{-1} = i\), where \(i\) is the imaginary unit.
2. Rewrite the square root of the negative number as \(\sqrt{-75} = \sqrt{-1 \times 75} = \sqrt{-1} \times \sqrt{75} = i \sqrt{75}\).
3. Simplify \(\sqrt{75}\) by factoring 75 into its prime factors: \$75 = 25 \times 3\(. Then, \)\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3}$.
4. Since \(\sqrt{25} = 5\), substitute back to get \(\sqrt{75} = 5 \sqrt{3}\). Therefore, the expression becomes \(i \times 5 \sqrt{3}\).
5. Combine the terms to write the simplified form as \$5i \sqrt{3}$.