Question

what is the following product?
\sqrt{12} \cdot \sqrt{18}
options:
\sqrt{30}
5\sqrt{6}
6\sqrt{6}
6\sqrt{5}

Explanation:

Step1: Use property of square roots

Recall that \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\) for non - negative real numbers \(a\) and \(b\). So, for \(\sqrt{12}\cdot\sqrt{18}\), we can rewrite it as \(\sqrt{12\times18}\).

Step2: Calculate the product inside the square root

First, calculate \(12\times18 = 216\). So now we have \(\sqrt{216}\).

Step3: Simplify the square root

We can factor \(216\) as \(36\times6\), since \(36\times6 = 216\). And \(\sqrt{36\times6}=\sqrt{36}\times\sqrt{6}\) (by the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) for \(a = 36\) and \(b = 6\)). Since \(\sqrt{36}=6\), we get \(6\sqrt{6}\).

Answer:

\(6\sqrt{6}\) (the option with \(6\sqrt{6}\))