Question

express in simplest radical form.

$-sqrt{6} + 9sqrt{24}$

Explanation:

Step1: Simplify $\sqrt{24}$

We know that $24 = 4\times6$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$). So $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$.

Step2: Substitute back into the original expression

The original expression is $-\sqrt{6}+9\sqrt{24}$. Substituting $\sqrt{24}=2\sqrt{6}$, we get $-\sqrt{6}+9\times(2\sqrt{6})$.

Step3: Simplify the second term

Calculate $9\times(2\sqrt{6}) = 18\sqrt{6}$. So the expression becomes $-\sqrt{6}+18\sqrt{6}$.

Step4: Combine like terms

Since $-\sqrt{6}$ and $18\sqrt{6}$ are like terms (both have $\sqrt{6}$), we can combine them: $(-1 + 18)\sqrt{6}=17\sqrt{6}$.

Answer:

$17\sqrt{6}$