How do you add radicals?

Answer 1

It does indeed seem like there should be a rule for adding radicals. There are rules for adding, subtracting, multiplying, and dividing whole numbers, and there are rules for multiplying and dividing radicals. However, there is no "rule" for adding radicals. For example, sqrt(2)+sqrt(3) does NOT equal sqrt(5), sqrt(6), or any other "radical" you could think of. In a professional research paper (and on any exam you may take) an answer of sqrt(2)+sqrt(3) would be a proper answer (assuming it is correct). However, a number like sqrt(4)+sqrt(1) can be simplified. This is simply 3.

Essentially, if a radical has no "nice square root" it cannot be simplified.

It is important to note, however, that an expression like sqrt(2)+sqrt(8) can be simplified. Since sqrt(8)=sqrt(4)sqrt(2)=2sqrt(2), the desired quantity could be simplified to 3sqrt(2).

I hope this was quite informative, and in time to help!