Terminology of different number representations

Question

Background:

I am writing an article and trying to find the proper words/terms for different representations of numbers. The article is regarding calculating the SIN, COS and TAN of a number of angles without getting decimal numbers because the "other" form is better for calculations when these are used in other formulas.

Here are two examples:

Two square roots of two can be written in the following two ways:

First: $$ 2\sqrt 2 $$

Second (floating point/decimal): $$ 2.82842712475 $$

Question

The second example is a decimal number.

What is the name for the representation of two square root of two in the first example?

Thanks!

Answer 1

When we write $2\sqrt{2}$ it's simply referred to the exact form.

Answer 2

In the case of the values of trigonometric functions that can be expressed symbolically, what you have is an algebraic expression (also called radical), which is a special case of a closed-form expression.

https://en.wikipedia.org/wiki/Closed-form_expression#Comparison_of_different_classes_of_expressions