Is the Book Wrong? - Square Root of 4

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Discussion Overview

The discussion revolves around the interpretation of the square root of 4 as presented in a textbook, specifically whether the textbook's assertion that the square root of 4 equals 2, and not negative 2, is correct. The scope includes mathematical reasoning and conceptual clarification regarding square roots and their definitions.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant questions the textbook's claim, suggesting it might be incorrect if it does not acknowledge that both 2 and -2 are solutions to the equation x² = 4.
  • Another participant proposes that the context might involve absolute values or specific conditions that could affect the interpretation of the square root.
  • A third participant notes that textbook authors often omit details, assuming readers understand the context, which may lead to confusion about the square root's definition.
  • Some participants clarify that while the square root of 4 is defined as the positive value (2), there are indeed two real numbers whose squares equal 4, namely 2 and -2.
  • One participant emphasizes that the square root function is defined to return the principal (positive) root, while acknowledging that solving the equation x² = 4 yields both positive and negative solutions.

Areas of Agreement / Disagreement

Participants express differing views on the textbook's accuracy and the interpretation of square roots. There is no consensus on whether the textbook is wrong, as some defend its definition while others highlight the potential for misunderstanding.

Contextual Notes

Participants note that the definition of the square root as the positive value may not encompass all mathematical contexts, particularly when solving equations where both positive and negative solutions exist.

Numbnut247
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hey guys on my textbook, it says that square root of 4 equals to 2 but not negative 2. The book is wrong right?
 
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What's the context? Maybe an absolute value symbol is hiding! Maybe its looking for solutions where a -2 would cause a divide by 0 or negative square root situation.
 
Just to extend on what Pengwuino said...

Textbook authors very often skip steps, or leave out what they feel to be implied information. Sometimes this is simply necessary if it's not relevant to the actual problem being discussed.

Physicists are notorious for doing this. They write math that may not be fully "correct," but they assume their readers know and understand the context of the mathematics.

For example, if a negative value doesn't make sense in the excerpt you're reading, the author assumed you knew and understood why s/he was discarding this value.

Unless the book you are reading is trying to teach you how to take the square root of something, then it's normal.. so get used to it ;)
 
Numbnut,

We have to take your word that the textbook said "square root" but I suspect it says [itex]\sqrt 4 = 2[/itex] (a true statement) while [tex]\sqrt 4 = -2[/tex] is definitely a false statement. However, there are, two real numbers whose squares are 4 ([itex]\sqrt 4 = 2[/itex] and [itex]-\sqrt 4 = -2[/itex]).
 
Last edited:
Tide said:
Numbnut,

We have to take your word that the textbook said "square root" but I suspect it says [itex]\sqrt 4 = 2[/itex] (a true statement) while [tex]\sqrt 4 = -2[/tex] is definitely a false statement. However, there are, two real numbers whose squares are 4 ([itex]\sqrt 4 = 2[/itex] and [itex]-\sqrt 4 = -2[/itex]).
But I think it's the part where (-2)^2 = 4 bothers him. Taking the square root of both sides...

But as was already mentioned, the context of the statement makes a difference.
 
Numbnut247 said:
hey guys on my textbook, it says that square root of 4 equals to 2 but not negative 2. The book is wrong right?

Your book is correct. The square root of a positive number a, is defined as the positive number x, such that x*x= a.


It is true that 2*2= 4 and that (-2)*(-2)= 4. Since 2 is the positive value the square root of 2 is 2.

Of course, if you were solving the equation x2= 4, you would have two answer: x= 2 and x= -2. That causes some people confusion.

Think of it this way: The solution to the equation x2= a (where a is a positive number) has to be written
[tex]x= \pm\sqrt{a}[/tex].
We have to have that "[itex]\pm[/itex]" precisely because [itex]\sqrt{a}[/itex] does not include the negative.
 

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