Question

simplify \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: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

\(\sqrt{75}=\sqrt{5^2\times3}=\sqrt{5^2}\times\sqrt{3}\)

Step3: Simplify \(\sqrt{5^2}\)

Since \(\sqrt{a^2}=a\) for \(a\geq0\), then \(\sqrt{5^2} = 5\). So \(\sqrt{75}=5\sqrt{3}\).

Answer:

\(5\sqrt{3}\)