Question

select the correct answer. simplify. \\(sqrt{75}\\) a. \\(3sqrt{5}\\) b. \\(15sqrt{5}\\) c. \\(25sqrt{3}\\) d. \\(5sqrt{3}\\)

Explanation:

Step1: Factor 75

We know that \(75 = 25\times3\), so \(\sqrt{75}=\sqrt{25\times3}\).

Step2: Use square - root property

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}\).
Since \(\sqrt{25} = 5\), then \(\sqrt{25}\times\sqrt{3}=5\sqrt{3}\).

Answer:

D. \(5\sqrt{3}\)