Question

What is the simplified form of the following expression?

Answer 1

Answer:

$\sqrt{3}$

Step-by-step explanation:

We will be using 2 properties of radicals in this simplification (outlined below).

• $\sqrt{a*b}=\sqrt{a}* \sqrt{b}$
• $\sqrt{a}*\sqrt{a}=a$

Let's simplify this:

$2\sqrt{27} +\sqrt{12} -3\sqrt{3}-2\sqrt{12}\\ =2\sqrt{9*3}+\sqrt{4*3} -3\sqrt{3}-2\sqrt{4*3} \\=2\sqrt{9} \sqrt{3} +\sqrt{4} \sqrt{3}-3\sqrt{3}-2\sqrt{4} \sqrt{3} \\=2(3)\sqrt{3}+(2)\sqrt{3} -3\sqrt{3}-2(2)\sqrt{3} \\ =6\sqrt{3} +2\sqrt{3}-3\sqrt{3}-4\sqrt{3} \\=\sqrt{3}$

First answer choice is right.