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2√20 - 3√7 - 2√5 + 4√63 = 2√(4 x 5) - 3√7 - 2√5 + 4√(9 x 7) = 4√5 - 2√5 - 3√7 + 12√7 = 2√5 + 9√7
5 - 2*sqrt(3) is already in simplest radical form, note that if you said 5 - sqrt(12) is definitely simplified to 5 - 2*sqrt(3).
3root(6)+5root(2) you really answered it yourself!
If the product of two irrationals is a rational, then they are both the same radical of a non-perfect square. For example, radical 5 times radical 5 is 5, since that is by definiton what a radical is.
6 radical 2