Question

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, \(\sqrt{32}=\sqrt{16\times2}\)

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can split the square root:
\(\sqrt{16\times2}=\sqrt{16}\times\sqrt{2}\)
Since \(\sqrt{16} = 4\) (because \(4^2 = 16\)), we substitute that in:
\(\sqrt{16}\times\sqrt{2}=4\sqrt{2}\)

Answer:

\(4\sqrt{2}\)