Question

Can someone help me with the attached file, please? Order what is in the file from least-to-greatest, with explanations, please. :D

Answer 1

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

Answer 2

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 :)