Answer:
√28 = 2√7
√40 = 2√10
√108 = 6√3
√125 = 5√5
-6√81 = -54
√80 = 4√5
3√60 = 6√15
-√200 = -10√2
4√320 = 32√5
Step-by-step explanation:
1. The largest factor that's a square in 28 is 4, so the other factor must be 7.
- [tex]\sqrt{28} = \sqrt{4} * \sqrt{7} = 2\sqrt{7}[/tex]
2. The largest factor that's a square in 40 is 4, so the other factor must be 10.
- [tex]\sqrt{40} = \sqrt{4} * \sqrt{10} = 2\sqrt{10}[/tex]
3. The largest factor that's a square in 108 is 36, so the other factor must be 3.
- [tex]\sqrt{108} = \sqrt{36} * \sqrt{3} = 6\sqrt{3}[/tex]
4. The largest factor that's a square in 125 is 25, so the other factor must be 5.
- [tex]\sqrt{125} = \sqrt{25} * \sqrt{5} = 5\sqrt{5}[/tex]
5. The square root of 81 is 9, and 9 times -6 is -54.
6. The largest factor that's a square in 80 is 16, so the other factor must be 5.
- [tex]\sqrt{80} = \sqrt{16} * \sqrt{5} = 4\sqrt{5}[/tex]
7. 3√60 is equivalent to √540 (because 60 x 9 = 540). The largest factor that's a square in 540 is 36, so the other factor must be 15.
- [tex]\sqrt{540} = \sqrt{36} * \sqrt{15} = 6\sqrt{15}[/tex]
8. The largest factor that's a square in 200 is 100, so the other factor must be 2.
- [tex]-\sqrt{200} = -\sqrt{100} * \sqrt{2} = -10\sqrt{2}[/tex]
9. 4√320 is equivalent to 5120 (because 320 x 16 equal 5120). The largest factor that's a square in 5120 is 1024, so the other factor must be 5.
- [tex]\sqrt{5120} = \sqrt{1024} * \sqrt{5} = 32\sqrt{5}[/tex]
