Question

simplify the expression: $2\sqrt{45} - 2\sqrt{5}$

Explanation:

Step1: Simplify $\sqrt{45}$

We know that $45 = 9\times5$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$). So $\sqrt{45}=\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$.

Step2: Substitute back into the original expression

The original expression is $2\sqrt{45}-2\sqrt{5}$. Substituting $\sqrt{45}=3\sqrt{5}$, we get $2\times3\sqrt{5}-2\sqrt{5}$.

Step3: Simplify the expression

First, calculate $2\times3\sqrt{5}=6\sqrt{5}$. Then the expression becomes $6\sqrt{5}-2\sqrt{5}$. Since the terms have the same radical part, we can combine them: $(6 - 2)\sqrt{5}=4\sqrt{5}$.

Answer:

$4\sqrt{5}$