To find the difference [tex]\(\sqrt{20} - \sqrt{80}\)[/tex], follow these steps:
1. Simplify the square roots:
- First, recognize that [tex]\(\sqrt{20}\)[/tex] can be simplified:
[tex]\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\][/tex]
- Similarly, simplify [tex]\(\sqrt{80}\)[/tex]:
[tex]\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\][/tex]
2. Substitute the simplified forms:
- Now that [tex]\(\sqrt{20}\)[/tex] is simplified to [tex]\(2\sqrt{5}\)[/tex] and [tex]\(\sqrt{80}\)[/tex] is simplified to [tex]\(4\sqrt{5}\)[/tex], substitute these back into the expression:
[tex]\[
\sqrt{20} - \sqrt{80} = 2\sqrt{5} - 4\sqrt{5}
\][/tex]
3. Calculate the difference:
- Combine the like terms:
[tex]\[
2\sqrt{5} - 4\sqrt{5} = (2 - 4)\sqrt{5} = -2\sqrt{5}
\][/tex]
So, the difference [tex]\(\sqrt{20} - \sqrt{80}\)[/tex] is [tex]\(-2\sqrt{5}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-2\sqrt{5}}
\][/tex]
