Question

express in simplest radical form.
$-sqrt{3} - 10sqrt{48}$

Explanation:

Step1: Simplify $\sqrt{48}$

Factor 48: $48 = 16\times3$. So, $\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}$.

Step2: Substitute back into the expression

The original expression is $-\sqrt{3}-10\sqrt{48}$. Substitute $\sqrt{48}=4\sqrt{3}$:
$-\sqrt{3}-10\times4\sqrt{3}=-\sqrt{3}-40\sqrt{3}$.

Step3: Combine like terms

Combine the terms with $\sqrt{3}$: $(-1 - 40)\sqrt{3}=-41\sqrt{3}$.

Answer:

$-41\sqrt{3}$