Question

simplify.
\sqrt{12} \cdot \sqrt{6}

Explanation:

Step1: Use property of square roots

Recall that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\) for \(a\geq0\), \(b\geq0\). So, \(\sqrt{12} \cdot \sqrt{6}=\sqrt{12\times6}\).

Step2: Calculate the product inside the square root

Calculate \(12\times6 = 72\), so we have \(\sqrt{72}\).

Step3: Simplify \(\sqrt{72}\)

Factor 72 into \(36\times2\), then \(\sqrt{72}=\sqrt{36\times2}\). Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) again, we get \(\sqrt{36}\cdot\sqrt{2}\). Since \(\sqrt{36} = 6\), this simplifies to \(6\sqrt{2}\).

Answer:

\(6\sqrt{2}\)