Question

subtract. write your answer in simplest form.
$2\sqrt{6} - 4\sqrt{150}$

Explanation:

Step1: Simplify \(\sqrt{150}\)

Factor 150: \(150 = 25\times6\), so \(\sqrt{150}=\sqrt{25\times6}=\sqrt{25}\times\sqrt{6}=5\sqrt{6}\) (since \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a\geq0,b\geq0\) and \(\sqrt{25} = 5\)).

Step2: Substitute back into the expression

The original expression is \(2\sqrt{6}-4\sqrt{150}\), substitute \(\sqrt{150}=5\sqrt{6}\) into it:
\(2\sqrt{6}-4\times(5\sqrt{6})=2\sqrt{6}-20\sqrt{6}\)

Step3: Combine like terms

Since \(2\sqrt{6}\) and \(- 20\sqrt{6}\) are like terms (they have the same radical part \(\sqrt{6}\)), we can combine them:
\((2 - 20)\sqrt{6}=-18\sqrt{6}\)

Answer:

\(-18\sqrt{6}\)