Question

simplify.
\sqrt{12}

Explanation:

Step1: Factor the radicand

We factor 12 into a product of a perfect square and another number. We know that \(12 = 4\times3\), where 4 is a perfect square (\(4 = 2^2\)). So we can rewrite \(\sqrt{12}\) as \(\sqrt{4\times3}\).

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 \(\sqrt{4\times3}\), we get \(\sqrt{4}\times\sqrt{3}\).

Step3: Simplify the perfect square root

Since \(\sqrt{4} = 2\) (because \(2^2=4\)), we substitute this back into the expression from Step 2. So \(\sqrt{4}\times\sqrt{3}=2\times\sqrt{3}\), which is written as \(2\sqrt{3}\).

Answer:

\(2\sqrt{3}\)