Question

question
express in simplest radical form.
$-7\sqrt{6} - 7\sqrt{96}$

Explanation:

Step1: Simplify \(\sqrt{96}\)

We factor 96 to find perfect square factors. \(96 = 16\times6\), so \(\sqrt{96}=\sqrt{16\times6}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 16\), \(b = 6\) and \(a\) is a perfect square), we get \(\sqrt{16\times6}=\sqrt{16}\times\sqrt{6}=4\sqrt{6}\).

Step2: Substitute back into the expression

The original expression is \(-7\sqrt{6}-7\sqrt{96}\). Substituting \(\sqrt{96}=4\sqrt{6}\), we have \(-7\sqrt{6}-7\times(4\sqrt{6})\).

Step3: Simplify the second term

Calculate \(7\times4\sqrt{6}=28\sqrt{6}\), so the expression becomes \(-7\sqrt{6}-28\sqrt{6}\).

Step4: Combine like terms

Since both terms have \(\sqrt{6}\), we can combine the coefficients: \((-7 - 28)\sqrt{6}\). Calculating \(-7-28=-35\), so the expression simplifies to \(-35\sqrt{6}\).

Answer:

\(-35\sqrt{6}\)