Question

simplify.

\\(\sqrt{75}\\)

\\(3\sqrt{5}\\)

\\(15\sqrt{5}\\)

\\(25\sqrt{3}\\)

\\(5\sqrt{3}\\)

Explanation:

Factor the radicand using the largest perfect square

$$ 75 = 25 \times 3 $$

Apply the product property of square roots

$$ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} $$

Simplify the perfect square

$$ \sqrt{25} \times \sqrt{3} = 5\sqrt{3} $$

Answer:

• (A) \(3\sqrt{5}\)
• (B) \(15\sqrt{5}\)
• (C) \(25\sqrt{3}\)
• (D) \(5\sqrt{3}\) (Correct answer)