Let's analyze each case and see if they are less than 8 first:
[tex]7<8,therefore(7)^{\frac{1}{2}}<8[/tex][tex]\sqrt[]{64}=8[/tex]
thus
[tex]\sqrt[]{60}<\sqrt[]{64}=8[/tex][tex]\sqrt[]{60}<8[/tex]
Finally,
[tex]64<80[/tex][tex]\sqrt[]{64}<\sqrt[]{80}[/tex]
thus
[tex]8<\sqrt[]{80}[/tex]
In sumary, the first two options are less than 8, but not the third.
Now let's see if they are greater than 6
[tex]9>7[/tex][tex]\sqrt[]{9}>\sqrt[]{7}[/tex][tex]3>\sqrt[]{7}[/tex]
and
[tex]6>3>\sqrt[]{7}[/tex]
thus
[tex]6>\sqrt[]{7}[/tex]
Now
[tex]36<60[/tex][tex]\sqrt[]{36}<\sqrt[]{60}[/tex]
and so
[tex]6<\sqrt[]{60}[/tex]
Finally
[tex]\sqrt[]{80}>\sqrt[]{60}>6[/tex]
thus
[tex]\sqrt[]{80}>6[/tex]
In conclussion, the second and third options are greater than 6, but not the first.
