Question

which expression is equivalent to \\(\sqrt{180}\\)?

\\(\bigcirc\\) \\(\sqrt{2 \cdot 2 \cdot 2 \cdot 3 \cdot 5}\\)
\\(\bigcirc\\) \\(\sqrt{2 \cdot 2 \cdot 3 \cdot 3 \cdot 5}\\)
\\(\bigcirc\\) \\(\sqrt{2 \cdot 2 \cdot 3 \cdot 5 \cdot 5}\\)
\\(\bigcirc\\) \\(\sqrt{2 \cdot 3 \cdot 3 \cdot 3 \cdot 5}\\)

Explanation:

Step1: Find prime factorization

$$180 = 2 \cdot 90 = 2 \cdot 2 \cdot 45 = 2 \cdot 2 \cdot 3 \cdot 15 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$$

Step2: Substitute into radical

$$\sqrt{180} = \sqrt{2 \cdot 2 \cdot 3 \cdot 3 \cdot 5}$$

Answer:

B. \(\sqrt{2 \cdot 2 \cdot 3 \cdot 3 \cdot 5}\)