Question

√7, 2, √8/2 order the number from least to greatest

Answer 1

To get a feel for where those two radicals fall on the number line, take a look at the perfect square roots they fall between. Both sqrt(7) and sqrt(8) fall between the perfect square roots sqrt(4) and sqrt(9); since sqrt(4) = 2 and sqrt(9) = 3, we know that sqrt(7) and sqrt(8) are somewhere in between 2 and 3. This means we know that sqrt(7) > 2. What about sqrt(8)/2 though? Well, sqrt(4)/2 = 2/2 = 1, and sqrt(9)/2 = 3/2 = 1 1/2, so sqrt(8)/2 has to be between 1 and 1 1/2, both of which are less than 2. Putting those all in order:

sqrt(8)/2, 2, sqrt(7)