You can do the same subtraction, division and deformation on two numbers, so it is easy to see whether the result of subtraction is greater than zero, equal to zero or less than zero.

For example:

( 1)√5-3-(√5-2 )/2

=[(2√5-6-(√5-2 )]/2

=(√5-4)/2

=(√5-√ 16)/2

& lt0

So) √5-3 is less than √5-2 divided by 2.

(2)√2/2-√3/3

=3√2/6-2√3/6

=(√ 18-√ 12)/6

& gt0

So √2 divided by 2 is greater than √3 divided by 3.