When should the plus/minus sign be used when dealing with square roots?

Click For Summary
The discussion revolves around the use of the plus/minus sign when solving equations involving square roots, particularly in the context of x² = 9. Participants debate whether the notation ± should be applied consistently when taking square roots, with some arguing that it can lead to confusion and contradictions in algebraic reasoning. The consensus suggests that while ± is a useful shorthand for indicating multiple solutions, it can also obscure the unique nature of solutions when not handled carefully. The conversation emphasizes the importance of understanding the underlying principles of equality and the behavior of square roots, particularly in relation to absolute values. Ultimately, clarity in notation and reasoning is deemed essential for accurate mathematical communication.
  • #31
Dr. Mirrage said:
So, then the only question I still have is when should I use the plus/minus sign?
When it makes things easier -- when it makes it easier for you to (correctly) solve a problem, when it makes it easier for you to explain something, and so forth.

If you don't find it makes things easier, then don't use it.
 

Similar threads

High School Principal square root of a complex number, why is it unique?
  • · Replies 13 ·
Replies
13
Views
6K
MHB How have I dropped a factor 2 on the square root of 19?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Not a "help need" but a question about "a self made square root formula"
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
  • · Replies 3 ·
Replies
3
Views
2K
High School Solving Square Root & Quadratic Equations
  • · Replies 6 ·
Replies
6
Views
2K
I have a quick question on square roots.
  • · Replies 9 ·
Replies
9
Views
1K
High School Problem with simple inequality
  • · Replies 13 ·
Replies
13
Views
2K
MHB Find the square roots of 4*sqrt(3)+4(i)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Reason for the irrationality of (most) square roots?
  • · Replies 12 ·
Replies
12
Views
2K
High School Square root of a negative number in a complex field
  • · Replies 45 ·
2
Replies
45
Views
5K