Is the Book Wrong? - Square Root of 4

[Numbnut247]

hey guys on my textbook, it says that square root of 4 equals to 2 but not negative 2. The book is wrong right?

 

[Pengwuino]

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.

 

[sporkstorms]

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 ;)

 

[Tide]

Numbnut,

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

 

[berkeman]

Numbnut,

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

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.

 

[HallsofIvy]

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
$$x= \pm\sqrt{a}$$.
We have to have that "$\pm$" precisely because $\sqrt{a}$ does not include the negative.