Y=X^1/2 is the same as Y=+/-sqrt(X) ?

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In summary, the conversation is discussing the statement from a textbook that Y=X^1/2 is equivalent to Y=+/-sqrt(X). There is a question about why 100^1/2 can also equal -10, and this is explained in terms of the principle that when solving for y, both positive and negative values should be considered. The author of the textbook is not named, but there is a suggestion to inform the author of the error for future editions.
  • #1
solve
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Y=X^1/2 is the same as Y=+/-sqrt(X) ??

Homework Statement




This is from a textbook:

Y=X^1/2 is the same as Y=+/-sqrt(X)

Homework Equations


The Attempt at a Solution



100^1/2=10

How is 100^1/2=-10 also true?

Thanks.
 
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  • #2
hi solve! :wink:
solve said:
This is from a textbook:

Y=X^1/2 is the same as Y=+/-sqrt(X)

Homework Equations


The Attempt at a Solution



100^1/2=10

How is 100^1/2=-10 also true?

Thanks.

you're right, it's wrong! :smile:

(which book?)
 
  • #3


tiny-tim said:
hi solve! :wink:


you're right, it's wrong! :smile:

(which book?)

Thank You for the answer, tiny-tim.

As for the book, I don't want to name it and make the otherwise excellent textbook look bad.
 
  • #4


solve said:
Thank You for the answer, tiny-tim.

As for the book, I don't want to name it and make the otherwise excellent textbook look bad.

Actually, you would be doing the author a favor by telling us the name and author of the book; that way, professionals could write to him/her about the error, so it could be fixed in subsequent editions.

RGV
 
  • #5


On the other hand, if the author is explaining how to solve y2 = x, for y, or solve y2 = 100 for y, then the answers are:
y = ± √(x) = ±(x)1/2 for y2 = x

y = ±10 for y2 = 100​
If this is the case you have only told us part of what the textbook was claiming, although the author may have also left a few details out of her/his explanation.
 

FAQ: Y=X^1/2 is the same as Y=+/-sqrt(X) ?

What is the equation Y=X^1/2?

The equation Y=X^1/2 represents a square root function, where the output (Y) is the square root of the input (X).

What is the difference between Y=X^1/2 and Y=+/-sqrt(X)?

There is no difference between these two equations. They both represent the same square root function, where the output can be either positive or negative.

Can Y=X^1/2 have a negative output?

Yes, Y=X^1/2 can have a negative output. This is because any number squared will result in a positive number, but taking the square root of a positive number can result in both a positive and negative value.

Can Y=X^1/2 be simplified further?

No, Y=X^1/2 is already in its simplest form. It represents the square root function, and any further simplification would change the meaning of the equation.

Is Y=X^1/2 the same as Y=X^(1/2)?

Yes, Y=X^1/2 and Y=X^(1/2) are both correct ways of writing the square root function. The parentheses in the second equation are not necessary but can help with clarity in more complex equations.

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