To find the difference between [tex]\(\sqrt{20}\)[/tex] and [tex]\(\sqrt{80}\)[/tex], follow these steps:
1. Calculate the square roots of 20 and 80 individually to get their approximate decimal values:
- [tex]\(\sqrt{20} \approx 4.47213595499958\)[/tex]
- [tex]\(\sqrt{80} \approx 8.94427190999916\)[/tex]
2. Subtract [tex]\(\sqrt{80}\)[/tex] from [tex]\(\sqrt{20}\)[/tex]:
- [tex]\(\sqrt{20} - \(\sqrt{80} \approx 4.47213595499958 - 8.94427190999916 = -4.47213595499958\)[/tex]
3. To confirm the result using simplified forms, express [tex]\(\sqrt{20}\)[/tex] and [tex]\(\sqrt{80}\)[/tex] in terms of [tex]\(\sqrt{5}\)[/tex]:
- [tex]\(\sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5}\)[/tex]
- [tex]\(\sqrt{80} = \sqrt{16 \times 5} = 4 \sqrt{5}\)[/tex]
4. Subtract the simplified terms:
- [tex]\(2 \sqrt{5} - 4 \sqrt{5} = (2 - 4) \sqrt{5} = -2 \sqrt{5}\)[/tex]
Therefore, the difference [tex]\(\sqrt{20} - \(\sqrt{80}\)[/tex] is [tex]\(-2\sqrt{5}\)[/tex].
The correct answer is [tex]\(-2 \sqrt{5}\)[/tex].
