Question

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

Explanation:

Step1: Factor 32 into perfect square and other

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 property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we have \(\sqrt{16\times2}=\sqrt{16}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{16}\)

Since \(\sqrt{16} = 4\) (because \(4^2 = 16\)), we substitute that in: \(4\times\sqrt{2}=4\sqrt{2}\).

Answer:

\(4\sqrt{2}\)