Question

which expression is equivalent to \\(\sqrt{116}\\)?

\\(\bigcirc\\) \\(8\sqrt{3}\\)
\\(\bigcirc\\) \\(4\sqrt{6}\\)
\\(\bigcirc\\) \\(13\\)
\\(\bigcirc\\) \\(2\sqrt{29}\\)

Explanation:

Step1: Factor the radicand

Find the prime factorization of \(116\).

$$116 = 4 \times 29 = 2^2 \times 29$$

Step2: Simplify the radical

Apply the product property of square roots.

$$\sqrt{116} = \sqrt{4 \times 29} = \sqrt{4} \times \sqrt{29} = 2\sqrt{29}$$

Answer:

\(2\sqrt{29}\)