Do not ever confuse x^1/2 with sqrt x

Do not ever confuse x^1/2 with sqrt x.

Because sqrtx is defined as principal sqrtx (positive).

Isnt that false? t. Math freshman
Post some articles for me to read up on

wrong

>math freshman
user, i...

On a similar note, do not confuse 0.999... with 1

Every nonnegative real number x has a unique nonnegative square root, called the **principal** square root, which is denoted by √x

Op is wrong, x^1/2 is defined as principal too! For example, 4^1/2=2 because of the notation.

This is correct.

The sqrt function is equivalent to the 1/2 power.

However, the solution to x^2 = a is
+-sqrt (a)

This is because the definition of
sqrt (x^2) = |x|

If we disregard the "principal" definition of sqrt and ^1/2, then why ((-2)^2)^1/2 = -2 if done in one way and 2 if done in another way?

this is bugging me

...

[math]
x^\frac{1}{2} = \sqrt{x} = \pm\sqrt{x}.
[/math]

>x√=±x√.
wrong

If we define x^1/2 = ±√x (it isn't but let's define that way), why does ((-2)^2)^1/2 = -2 if done in one way and 2 if done in another way?

+√1 = +1; -1
-√1 = -1; +1

The definition of the symbol sqrt is that it is the principal root (positive).

You are failing to distinguish two cases
1) the function "the square root of"
2) taking square roots to solve equations

functions NEVER have more than one value for a given input

but an equation MAY have multiple solutions

can you give an example?

The equation x^2 = 4 has solutions x = 2 and x = -2.

However, sqrt (4) = |2| = 2

The difference is that when you solve the equation x^2 = 4, you get
|x| = 2
Which has solutions x = +-2

But the square root itself is always |x| which is positive regardless of the sign of x.

guessing, it goes in the same direction as

Adding to myself:

sqrt(2) * sqrt(2) = 2
2^(0.5) * 2^(0.5) = 2
2^(0.5 + 0.5) = 2
2 = 2

I don't understand why people feel the urge to prove math wrong. If something was wrong somebody would have noticed. And it would not have been this late with such fundemental things and not by people on Veeky Forums.

number writing system is utterly broken.
cant we come up with writing system that arent confusing and can express all operations without extra symbols?