Question

express in simplest radical form.
$-3\sqrt{108} + 4\sqrt{3}$
answer
attempt 1 out of 2

Explanation:

Step1: Simplify $\sqrt{108}$

Factor 108: $108 = 36\times3$. So, $\sqrt{108}=\sqrt{36\times3}=\sqrt{36}\times\sqrt{3}=6\sqrt{3}$.

Step2: Substitute back into the original expression

The original expression is $-3\sqrt{108}+4\sqrt{3}$. Substituting $\sqrt{108}=6\sqrt{3}$, we get $-3\times6\sqrt{3}+4\sqrt{3}$.

Step3: Simplify the terms

Calculate $-3\times6\sqrt{3}=-18\sqrt{3}$. Now the expression is $-18\sqrt{3}+4\sqrt{3}$.

Step4: Combine like terms

Combine the coefficients: $-18 + 4=-14$. So the result is $-14\sqrt{3}$.

Answer:

$-14\sqrt{3}$