One way is to use calculator the other way is to use common sense
some common sense stuff is fractions are likely at the bottom 12 is probably at top put the ones that you know in order and solve the rest
ok so put the obvius ones on top 12 is top
we have to compare fractions, square roots, and whle numbers
to compare the fracitons it is easy to compare the square roots, lets say you wanted to see whether √12 or 4.2 was bigger what you would do is 4.2^2 and see if that is bigger or smaller than 12 (it is bigger)
so, I will do it from lowest to greatest
1/2 and √2 compare for bottom spot 1/2^2=1/4 1/4<2 1/2 is bottom followed by √2 (so far 1/2,√2)
then next, 3/2=1 and 1/2 so that is next (so far 1/2, √2, 3/2)
ok, we know that √9=3 so that is next (so far 1/2,√2, 3/2,√9)
compare √12 with 3.56 3.56^2=12.67 12.67>12 then the next one up is √12 then 3.56 (so far 1/2,√2, 3/2, √9, √12, 3.56)
compare 4.03, 4.2, and √17 4.03^2=16.24 16.24<17 4.2^2=17.64 17.64>17 so they are 4.03,√17, 4.2 (so far 1/2, √2, 3/2, √9, √12, 3.56, 4.03, √17, 4.2)
and obiously 12 is last
the order is 1/2, √2, 3/2, √9, √12, 3.56, 4.03, √17, 4.2, 12 using logic
I would start by converting everything into decimal, as it makes it a LOT easier to understand.
So, you should be able use a calculator to convert the square roots and fractions into decimal. Let's start.
Square root 12 is equivalent to 3.46 (to 2 decimal places)
Square root 9 is 3 (you should know that because 3 × 3 = 9)
12 is already in decimal so it's just 12
3.56, 4.03 and 4.2 are also in decimal so you leave them
Square root 17 is 4.12 (to 2 decimal places)
Square root 2 is 1.41 (also 2 decimal places)
1/2 is the same as 0.5 (once again, you should know that)
And 3/2 is the same as 3 ÷ 2, which is 1.5.
So in order of least to greatest, it's:
1/2, square root of 2, 3/2, square root of 9, square root of 12, 3.56, 4.03, square root of 17. 4.2 and finally 12.
Hope this helps :)
