Question

express in simplest radical form.\\(\sqrt{32}\\)

Explanation:

Step1: Factor the radicand

We factor 32 into a product of a perfect square and another number. We know that \(32 = 16\times2\), where 16 is a perfect square (\(16 = 4^2\)). So we can rewrite \(\sqrt{32}\) as \(\sqrt{16\times2}\).

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 \(\sqrt{16\times2}\), we get \(\sqrt{16}\times\sqrt{2}\).

Step3: Simplify the perfect square root

Since \(\sqrt{16} = 4\) (because \(4^2 = 16\)), we substitute this back into the expression from Step 2. So we have \(4\times\sqrt{2}\), which is written as \(4\sqrt{2}\).

Answer:

\(4\sqrt{2}\)