Question

what do you get when you simplify the expression below completely?
$3\sqrt{6} \times (-2)\sqrt{6}$
$\circ -6\sqrt{36}$
$\circ 1\sqrt{36}$
$\circ -36$
$\circ -6\sqrt{6}$

Explanation:

Step1: Multiply the coefficients and the radicals separately

First, multiply the coefficients \(3\) and \(-2\), and multiply the radicals \(\sqrt{6}\) and \(\sqrt{6}\) separately. So we have \(3\times(-2)\times\sqrt{6}\times\sqrt{6}\).

Step2: Calculate the product of coefficients and the product of radicals

The product of the coefficients \(3\times(-2)= - 6\). For the radicals, using the property \(\sqrt{a}\times\sqrt{a}=a\) (when \(a\geq0\)), we have \(\sqrt{6}\times\sqrt{6} = 6\). So now the expression becomes \(-6\times6\).

Step3: Multiply the remaining numbers

Calculate \(-6\times6=-36\).

Answer:

\(-36\) (corresponding to the option " \(-36\)")