Here is a nice graphing scientific calculator type app from KDE in Ubuntu. I have been mainly using this as a graphing/scientific calculator for sin, cos, etc. It doesn't have and explicit square root function, but you can always do ^(1/2) or any other power. It has a nice autofill/autosearch feature. That is, when you begin to type it brings up a list of functions based on your input. Fro example, type "arc" and it brings up "arcsin, arccos, etc."
KAlgebra is a fully featured calculator that lets you plot different types of 2D and 3D functions and to calculate easy and not so easy calculations, such as addition, trigonometric functions or derivatives.
The application has been thought to be easily understandable for students, so that they don't need to read a boring manual. The language is deeply integrated in the UI, providing a dictionary with representations for all the available operations, code highlighting and code completion.
My screenshot:
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