Question

express in simplest radical form. $sqrt{96}+7sqrt{24}$

Explanation:

Step1: Simplify $\sqrt{96}$

We find the prime - factorization of 96: $96 = 16\times6$. Then $\sqrt{96}=\sqrt{16\times6}=\sqrt{16}\times\sqrt{6}=4\sqrt{6}$ according to the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 16\geq0$, $b = 6\geq0$).

Step2: Simplify $\sqrt{24}$

Find the prime - factorization of 24: $24=4\times6$. Then $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$ according to the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 4\geq0$, $b = 6\geq0$).

Step3: Combine like terms

$\sqrt{96}+7\sqrt{24}=4\sqrt{6}+7\times2\sqrt{6}=4\sqrt{6}+14\sqrt{6}=(4 + 14)\sqrt{6}=18\sqrt{6}$.

Answer:

$18\sqrt{6}$