Question

$\sqrt{75}$

Explanation:

Step1: Factor 75 into prime factors

We know that \(75 = 25\times3\), and \(25 = 5^{2}\), so \(75=5^{2}\times3\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we have \(\sqrt{75}=\sqrt{5^{2}\times3}=\sqrt{5^{2}}\times\sqrt{3}\). Since \(\sqrt{5^{2}} = 5\), then \(\sqrt{75}=5\sqrt{3}\).

Answer:

\(5\sqrt{3}\)