Question

subtract. write your answer in simplest form.
$2\sqrt{3} - 8\sqrt{12}$

Explanation:

Step1: Simplify \(\sqrt{12}\)

We know that \(12 = 4\times3\), so \(\sqrt{12}=\sqrt{4\times3}\). By the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{4\times3}=\sqrt{4}\times\sqrt{3} = 2\sqrt{3}\).

Step2: Substitute back into the expression

The original expression is \(2\sqrt{3}-8\sqrt{12}\). Substituting \(\sqrt{12} = 2\sqrt{3}\) into it, we get \(2\sqrt{3}-8\times(2\sqrt{3})\).

Step3: Simplify the expression

First, calculate \(8\times(2\sqrt{3})=16\sqrt{3}\). Then the expression becomes \(2\sqrt{3}-16\sqrt{3}\). Combining like terms, \((2 - 16)\sqrt{3}=- 14\sqrt{3}\).

Answer:

\(-14\sqrt{3}\)