Question

add. write your answer in simplest form.
$-4sqrt{24} + 8sqrt{54}$

Explanation:

Step1: Simplify each square root

First, factor the radicands (the numbers inside the square roots) into perfect squares and other factors. For $\sqrt{24}$, we have $24 = 4\times6$, where $4$ is a perfect square. So, $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$. Then, for $\sqrt{54}$, we factor $54 = 9\times6$, and $9$ is a perfect square. So, $\sqrt{54}=\sqrt{9\times6}=\sqrt{9}\times\sqrt{6}=3\sqrt{6}$.

Now substitute these back into the original expression: $-4\sqrt{24}+8\sqrt{54}=-4\times(2\sqrt{6})+8\times(3\sqrt{6})$.

Step2: Multiply the coefficients

Calculate the products: $-4\times2\sqrt{6}=-8\sqrt{6}$ and $8\times3\sqrt{6}=24\sqrt{6}$.

Step3: Combine like terms

Now we have $-8\sqrt{6}+24\sqrt{6}$. Since the square roots are the same ($\sqrt{6}$), we can combine the coefficients: $(-8 + 24)\sqrt{6}=16\sqrt{6}$.

Answer:

$16\sqrt{6}$