General Question About Square Roots

[hkparikh09]

Will use a simple example.

In a data sufficiency question:

(4)^(1/2) = X

What is the value of X?

Is +2 the only possible value for X, or can X also equal -2?

2 * 2 = 4
-2 * -2 = 4

So the principle I'm not sure of is: can the square root of a positive # be negative?

[RonPurewal]

If you see the "√" sign, or the exponent 1/2, then you're talking about the positive value.

This DOES NOT mean that the negative value can't also be squared to give the same number.

In fact, it's not an issue of math at all; it's an issue of symbols.
Symbols can only mean one thing. If a symbol could mean two different things, it would be useless.
(Useless in mathematics, anyway; ambiguity is a pretty cool thing in, say, poetry.)

For instance, how long is the diagonal of a square whose sides are 1 unit long?
You probably said "√2".
Now, think about why you can say that: because "√2" unambiguously represents the positive root.
If "√" could refer to either root, then it would actually be impossible to write this number!

[RonPurewal]

If there is confusion here, then that confusion exists because you're thinking about an equation to be solved.
E.g., "x^2 = 4. What are the possible values of x?"

In this case, both 2 and -2.
The entire issue above"”the symbol"”is a non-issue here. There's no "√" anywhere in the problem statement (unless you introduce it while solving); we just want to find all the different values that do this.

[hkparikh09]

This helps a lot. Thank you!

[RonPurewal]

You're welcome.