Question

which expression is equivalent to \\(10\sqrt{5}\\)?

\\(\bigcirc\\ \sqrt{500}\\)
\\(\bigcirc\\ \sqrt{105}\\)
\\(\bigcirc\\ \sqrt{50}\\)
\\(\bigcirc\\ \sqrt{15}\\)

Explanation:

Express the coefficient as a square root

$$ 10 = \sqrt{10^2} = \sqrt{100} $$

Multiply the radicands

$$ 10\sqrt{5} = \sqrt{100} \cdot \sqrt{5} = \sqrt{100 \cdot 5} = \sqrt{500} $$

Answer:

• (A) \(\sqrt{500}\) (Correct answer)
• (B) \(\sqrt{105}\)
• (C) \(\sqrt{50}\)
• (D) \(\sqrt{15}\)