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It depends on which square roots. I think some examples will help. I will write S(2) to mean the square root of 2 for this answer. So S(2)+S(2)=2S(2). There is no other way to combine them. However, S(8)+S(2)=S(4x2)+S(2)=2S(2)+S(2)=3S(2) So you can combine. Basically, you combine like terms and whenever possible try to create like terms. If you had S(21)+S(19), they are NOT like terms and there is nothing more you can combine. You are done.

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Q: How do you add 2 square roots together?
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How do you add simplified square roots?

You can add simplified square roots only if the radicals are the same and, in that case, you treat the radicals as you would treat a variable in algebra.For example, sqrt(18) + sqrt(50)= sqrt(9*2) + sqrt(25*2)= 3*sqrt(2) + 5*sqrt(2)= [3 + 5]*sqrt(2)= 8*sqrt(2)


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