Question

simplify the expression: $3\sqrt{45} + 3\sqrt{20}$

Explanation:

Step1: Simplify each square root

First, we simplify $\sqrt{45}$ and $\sqrt{20}$ by factoring out perfect squares.
For $\sqrt{45}$, we know that $45 = 9\times5$, and $\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$ (since $\sqrt{9} = 3$). So, $3\sqrt{45}=3\times3\sqrt{5}=9\sqrt{5}$.
For $\sqrt{20}$, we know that $20 = 4\times5$, and $\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}$ (since $\sqrt{4} = 2$). So, $3\sqrt{20}=3\times2\sqrt{5}=6\sqrt{5}$.

Step2: Combine like terms

Now we have $9\sqrt{5}+6\sqrt{5}$. Since both terms have $\sqrt{5}$, we can combine the coefficients: $9 + 6 = 15$. So, $9\sqrt{5}+6\sqrt{5}=15\sqrt{5}$.

Answer:

$15\sqrt{5}$