Question

select the correct answer.
what is \\(\sqrt{125}\\) in simplest form?
\\(\bigcirc\\) a. \\(\\ 5\sqrt{5}\\)
\\(\bigcirc\\) b. \\(\\ 25\sqrt{5}\\)
\\(\bigcirc\\) c. \\(\\ 5\sqrt{25}\\)
\\(\bigcirc\\) d. \\(\\ 15\\)

Explanation:

Step1: Factor 125 into prime factors

We know that \(125 = 25\times5\), and \(25 = 5^2\). So, \(125=5^2\times5\).

Step2: Apply square - root property

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{125}=\sqrt{5^2\times5}\).
Then, using the property \(\sqrt{a^2}=a\) (\(a\geq0\)), we get \(\sqrt{5^2\times5}=\sqrt{5^2}\times\sqrt{5}\).
Since \(\sqrt{5^2} = 5\), then \(\sqrt{5^2}\times\sqrt{5}=5\sqrt{5}\).

Answer:

A. \(5\sqrt{5}\)