Lets check the validity of each one of our statements:
Statement A is false. The square root of a number less than 1 is greater than the number itself. In fact, [tex] \sqrt{ \frac{4}{5} } = \sqrt{0.8} =0.89[/tex]. Since [tex]0.89[/tex] is greater than [tex]0.8[/tex], [tex] \sqrt{0.8} [/tex] is greater than [tex] \frac{4}{5} [/tex]; therefore, statement A is false.
Statement B is false. The square root of a number greater than 1 is less than the number itself. in fact, [tex] \sqrt{7} =2.64[/tex], whereas [tex] \sqrt{7^2} =7[/tex]. Since 2.64 is less than 7, [tex] \sqrt{7} [/tex] is less than [tex] \sqrt{7^2} [/tex]; therefore statement B is false.
Statement C is false. [tex] \sqrt{7} [/tex] is actually less than 7 divided by two, so there is no way that [tex] \sqrt{7} [/tex] is between 6 and 8. In fact [tex] \sqrt{7} =2.64[/tex]. Since 5 is greater than 2.64, [tex]( \sqrt{5} )^2[/tex] is greater than [tex] \sqrt{7} [/tex]; therefore, statement C is false.
Statement D is true. [tex] \sqrt{7} =2.64[/tex]. Since 2.64 is greater than 0.8, [tex] \sqrt{7} [/tex] is greater than [tex] \frac{4}{5} [/tex].
We can conclude that Jana should use statement D to create her list; also the correct order from least to greatest is: [tex] \frac{4}{5} [/tex], [tex] \sqrt{0.8} [/tex],[tex] \sqrt{7} [/tex], [tex]( \sqrt{5} )^2[/tex], [tex] \sqrt{7^2} [/tex]
