Question

subtract. write your answer in simplest form.
$-8sqrt{6} - 3sqrt{54}$

Explanation:

Step1: Simplify $\sqrt{54}$

Factor 54: $54 = 9\times6$, so $\sqrt{54}=\sqrt{9\times6}=\sqrt{9}\times\sqrt{6}=3\sqrt{6}$ (since $\sqrt{9}=3$).

Step2: Substitute back into the expression

The original expression is $-8\sqrt{6}-3\sqrt{54}$. Substitute $\sqrt{54}=3\sqrt{6}$:
$-8\sqrt{6}-3\times(3\sqrt{6})=-8\sqrt{6}-9\sqrt{6}$

Step3: Combine like terms

Since both terms have $\sqrt{6}$, we combine the coefficients: $-8 - 9=-17$, so $-8\sqrt{6}-9\sqrt{6}=-17\sqrt{6}$.

Answer:

$-17\sqrt{6}$