Question

question
express in simplest radical form.
\\(sqrt{75}\\)

Explanation:

Step1: Factor 75 into factors

We know that \(75 = 25\times3\), and 25 is a perfect square. So we can rewrite \(\sqrt{75}\) as \(\sqrt{25\times3}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

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

Step3: Simplify \(\sqrt{25}\)

Since \(\sqrt{25} = 5\), then \(\sqrt{25}\times\sqrt{3}=5\sqrt{3}\).

Answer:

\(5\sqrt{3}\)