Question

subtract. simplify by collecting like radical terms, if possible.
\\(\sqrt{45} - \sqrt{20}\\)
\\(\sqrt{45} - \sqrt{20} = \square\\)
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify $\sqrt{45}$

Factor 45 into $9\times5$, so $\sqrt{45}=\sqrt{9\times5}$. Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 9$, $b = 5$ and $\sqrt{9}=3$), we get $\sqrt{45}=3\sqrt{5}$.

Step2: Simplify $\sqrt{20}$

Factor 20 into $4\times5$, so $\sqrt{20}=\sqrt{4\times5}$. Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 4$, $b = 5$ and $\sqrt{4}=2$), we get $\sqrt{20}=2\sqrt{5}$.

Step3: Subtract the simplified radicals

Now we have $3\sqrt{5}-2\sqrt{5}$. Since they are like radical terms (same radical part $\sqrt{5}$), we subtract the coefficients: $(3 - 2)\sqrt{5}=\sqrt{5}$.

Answer:

$\sqrt{5}$