Question

subtract. write your answer in simplest form.
$7\sqrt{96} - \sqrt{6}$

Explanation:

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

Factor 96: \( 96 = 16 \times 6 \), so \( \sqrt{96} = \sqrt{16 \times 6} \). Using the property \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (for \( a\geq0, b\geq0 \)), we get \( \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6} \).

Step2: Substitute back into the expression

The original expression is \( 7\sqrt{96} - \sqrt{6} \). Substituting \( \sqrt{96} = 4\sqrt{6} \), we have \( 7\times4\sqrt{6} - \sqrt{6} \).

Step3: Simplify the coefficients

Calculate \( 7\times4 = 28 \), so the expression becomes \( 28\sqrt{6} - \sqrt{6} \). Now, combine like terms: \( (28 - 1)\sqrt{6} = 27\sqrt{6} \).

Answer:

\( 27\sqrt{6} \)