For the first problem, substitute w=y^2 and then you have a quadratic equation in w, which you can easily solve. Once you find the two values for w, then y = +/- sqrt(w).

For the next few rearrange so that you can square and get rid of the square root signs. For example starting with:

sqrt{3s+4}+2s=12, bring the 2s term to the right and square both sides to get 3s+4=(12-2s)^2

= 144-48s+4s^2. Now you can solve as usual.

For the last two square both sides, and you'll end up with a square root term. Rearrange to get that term by itself, and as above square again and rearrange. Also consider doing the w=x^2 substitution to get a quadratic. Hope this helps.