since this is an inequality or a simple boolean statement, you can also use equivalencies - 1 == sqrt(1) to simply do a quick proof of true/false

sqrt(6) - sqrt(2) < sqrt(1) becomes

6^1/2 - 2^1/2 < 1^1/2

you can then consider the power 1/2 almost as a variable - the same as an imaginary number... and since the variables are all common, it becomes the coefficient that is the determining factor

6^1/2 - 2^1/2 = 4^1/2

sqrt(4) = 2

2 < 1