the nominal square root

(suggested new terminology)
definition: the nominal square root of x^2 is x.
definition: the actual square root is, in light of the existence of the nominal square root, a retronym for the (traditional) square root, that is, the actual square root of a nonnegative real real number x is that (unique) nonnegative number y such that x = y^2.
observation: nominal square roots obey the same manipulation-laws as actual square roots. for example, the nominal square root of a quotient is the quotient of the nominal square roots.
observation: for a binomial, the nominal square root and the actual square root are equal.
observation: if a binomial is a perfect square, then it contains at least one numeric literal.
note: during the course of the derivation of the quadratic formula, there is a certain step at which the nominal square root of a certain quotient is taken. the numerator is a binomial, and so we just put it under the square-root sign, but the denominator is a perfect square, and so its nominal square root is not equal to its actual square root. taking the nominal square root instead of the actual square root allows the derivation to go through without having to consider two separate cases of the algebraic sign of the leading coefficient.
keywords: mathematics, numeric literals
The text passage introduces and defines the concept of "nominal square root" and contrasts it with the "actual square root," providing observations and a note on its application in the derivation of the quadratic formula.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
the nominal square root

(suggested new terminology)
definition: the nominal square root of x^2 is x.
definition: the actual square root is, in light of the existence of the nominal square root, a retronym for the (traditional) square root, that is, the actual square root of a nonnegative real real number x is that (unique) nonnegative number y such that x = y^2.
observation: nominal square roots obey the same manipulation-laws as actual square roots. for example, the nominal square root of a quotient is the quotient of the nominal square roots.
observation: for a binomial, the nominal square root and the actual square root are equal.
observation: if a binomial is a perfect square, then it contains at least one numeric literal.
note: during the course of the derivation of the quadratic formula, there is a certain step at which the nominal square root of a certain quotient is taken. the numerator is a binomial, and so we just put it under the square-root sign, but the denominator is a perfect square, and so its nominal square root is not equal to its actual square root. taking the nominal square root instead of the actual square root allows the derivation to go through without having to consider two separate cases of the algebraic sign of the leading coefficient.
keywords: mathematics, numeric literals
user
The text passage introduces and defines the concept of "nominal square root" and contrasts it with the "actual square root," providing observations and a note on its application in the derivation of the quadratic formula.

TYPE: NO_QUESTION