Question

subtract. write your answer in simplest form.
$-3sqrt{5} - 6sqrt{20}$

Explanation:

Step1: Simplify $\sqrt{20}$

We know that $20 = 4\times5$, so $\sqrt{20}=\sqrt{4\times5}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 4$ and $b = 5$), we have $\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}$.

Step2: Substitute back into the original expression

The original expression is $- 3\sqrt{5}-6\sqrt{20}$. Substituting $\sqrt{20} = 2\sqrt{5}$ into the expression, we get $-3\sqrt{5}-6\times(2\sqrt{5})$.

Step3: Simplify the second term

Calculate $6\times(2\sqrt{5}) = 12\sqrt{5}$. So the expression becomes $-3\sqrt{5}-12\sqrt{5}$.

Step4: Combine like terms

Since both terms have $\sqrt{5}$, we can combine them. Using the rule $a\sqrt{c}+b\sqrt{c}=(a + b)\sqrt{c}$, here $a=-3$ and $b = - 12$, so $(-3-12)\sqrt{5}=-15\sqrt{5}$.

Answer:

$-15\sqrt{5}$