Given numbers : [tex]\sqrt{64} ,\ 8\frac{1}{7} , \ 8.141414... , \ \frac{15}{2}[/tex]
[tex]\sqrt{64} = \sqrt{2*2*2*2*2*2}[/tex]
A pair of a number inside square root give a number out of square root.
We have three pairs of 2's are there.
Therefore,
[tex]\sqrt{64} = \sqrt{2*2*2*2*2*2}=2*2*2=8[/tex]
[tex]8 \frac{1}{7}=8.142857....[/tex] ( Because 1/7 = 0.142857....)
8.14..... = 8.141414....
[tex]\frac{15}{2}=7.5[/tex] (dividing 15 by 2 we get 7.5)
We can cleary see 7.5 is smallest number, second smaller is 8, and third one is 8.141414.... and finally fourth 8.142857.....
Subsituting original given numbers, we get
least to greatest :
[tex]\frac{15}{2}, \ \sqrt{64} , \ 8.141414...,\ 8\frac{1}{7}[/tex]
