what is the following product?\n$sqrt{12}cdotsqrt{18}$\n$sqrt{30}$\n$5sqrt{6}$\n$6sqrt{5}$\n$6sqrt{6}$

Explanation:

Step1: Simplify square - roots

First, simplify $\sqrt{12}$ and $\sqrt{18}$. $\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}$ $\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$

Step2: Calculate the product

Then, find the product of $\sqrt{12}$ and $\sqrt{18}$, which is now $(2\sqrt{3})\times(3\sqrt{2})$. Using the property of multiplication of radicals $a\sqrt{m}\times b\sqrt{n}=ab\sqrt{mn}$, we have $(2\sqrt{3})\times(3\sqrt{2})=(2\times3)\sqrt{3\times2}=6\sqrt{6}$

Answer:

$6\sqrt{6}$