Question

select the correct answer.

what is the simplified form of \\(\sqrt{45}\\)?

\\(\bigcirc\\ \sqrt{5}\\)
\\(\bigcirc\\ \sqrt{9 \cdot 5}\\)
\\(\bigcirc\\ 3\sqrt{5}\\)
\\(\bigcirc\\ 5\sqrt{3}\\)

Explanation:

Factor the radicand using the largest perfect square

$$ 45 = 9 \times 5 $$

Apply the product property of square roots

$$ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} $$

Simplify the square root of the perfect square

$$ \sqrt{9} \times \sqrt{5} = 3\sqrt{5} $$

Answer:

• (A) \(\sqrt{5}\)
• (B) \(\sqrt{9 \cdot 5}\)
• (C) \(3\sqrt{5}\) (Correct answer)
• (D) \(5\sqrt{3}\)