Question

add. write your answer in simplest form. -9√5 + 6√125

Explanation:

Step1: Simplify $\sqrt{125}$

Factor 125: $125 = 25\times5$, so $\sqrt{125}=\sqrt{25\times5}=\sqrt{25}\times\sqrt{5}=5\sqrt{5}$ (using $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ for $a\geq0,b\geq0$).

Step2: Substitute back and simplify

Original expression: $-9\sqrt{5}+6\sqrt{125}$. Substitute $\sqrt{125}=5\sqrt{5}$: $-9\sqrt{5}+6\times5\sqrt{5}=-9\sqrt{5}+30\sqrt{5}$.
Combine like terms: $(-9 + 30)\sqrt{5}=21\sqrt{5}$.

Answer:

$21\sqrt{5}$