Question

question 9
1 pts
simplify: $4\sqrt{8} - 3\sqrt{8} - 8\sqrt{72}$
$\circ -54\sqrt{5}$
$\circ -14\sqrt{2}$
$\circ$ cannot be simplified
$\circ -46\sqrt{2}$

Explanation:

Step1: Simplify like radicals first

First, combine the terms with $\sqrt{8}$. We have $4\sqrt{8}-3\sqrt{8}=(4 - 3)\sqrt{8}=\sqrt{8}$.

Step2: Simplify $\sqrt{8}$ and $\sqrt{72}$

Simplify $\sqrt{8}$: $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$.
Simplify $\sqrt{72}$: $\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}$.
Now our expression becomes $\sqrt{8}-8\sqrt{72}=2\sqrt{2}-8\times(6\sqrt{2})$.

Step3: Calculate the remaining terms

Calculate $8\times(6\sqrt{2}) = 48\sqrt{2}$. Then we have $2\sqrt{2}-48\sqrt{2}=(2 - 48)\sqrt{2}=- 46\sqrt{2}$.

Answer:

$-46\sqrt{2}$ (corresponding to the option with text “$-46\sqrt{2}$”)