Question

question
express in simplest radical form.
\\(\sqrt{28}\\)

Explanation:

Step1: Factor the radicand

We factor 28 into a product of a perfect square and another number. We know that \(28 = 4\times7\), where 4 is a perfect square (\(4 = 2^2\)). So we can rewrite \(\sqrt{28}\) as \(\sqrt{4\times7}\).

Step2: Use the property of square roots

The property of square roots states that \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a\geq0\) and \(b\geq0\). Applying this property to \(\sqrt{4\times7}\), we get \(\sqrt{4}\times\sqrt{7}\).

Step3: Simplify \(\sqrt{4}\)

Since \(\sqrt{4} = 2\) (because \(2^2 = 4\)), we substitute this back into the expression from Step 2. So \(\sqrt{4}\times\sqrt{7}=2\times\sqrt{7}=2\sqrt{7}\).

Answer:

\(2\sqrt{7}\)