Question

subtract. write your answer in simplest form.
$7\sqrt{6} - 3\sqrt{54}$

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 $7\sqrt{6}-3\sqrt{54}$. Substitute $\sqrt{54}=3\sqrt{6}$: $7\sqrt{6}-3\times(3\sqrt{6}) = 7\sqrt{6}-9\sqrt{6}$.

Step3: Combine like terms

$7\sqrt{6}-9\sqrt{6}=(7 - 9)\sqrt{6}=-2\sqrt{6}$.

Answer:

$-2\sqrt{6}$