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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!

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  • $\begingroup$ Additionally, "simplest radical form" also seems to be an answer. $\endgroup$ – varlogtim May 20 '18 at 22:00
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    $\begingroup$ One should note that 2\sqrt 2 \neq 2.82842712475$. $\endgroup$ – Shalop May 20 '18 at 22:23
  • $\begingroup$ Another form: $\sqrt{8}$ $\endgroup$ – Hurkyl May 20 '18 at 23:19
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When we write $2\sqrt{2}$ it's simply referred to the exact form.

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    $\begingroup$ Another option would be "symbolic". $\endgroup$ – Henning Makholm May 20 '18 at 21:36
  • $\begingroup$ Thanks Sean! This is the google search I needed! :) Just to add to this, a few definitions I read of "exact form" were that an "exact number" has a certain value, it cannot be simplified, and there are an infinite amount of significant digits. $\endgroup$ – varlogtim May 20 '18 at 21:37
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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

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