# If y^2 = 4, then why do we get two values +2 and -2 of 'y'?

#### Indranil

##### Junior Member
If y^2 = 4, then why do we get two values +2 and -2 of 'y'?
y^2 = 4,
y = +2 and y = -2

#### mmm4444bot

##### Super Moderator
Staff member
Because both 2^2 and (-2)^2 equal 4, and we're looking for all Real solutions.

Let's solve the equation y^2 = 4, by taking the square root of each side.

sqrt(y^2) = sqrt(4)

The square root of y^2 is not y; it is |y|. So the equation simplifies to:

|y| = 2

The rule for removing the absolute value symbols is to consider both roots.

y = ±2

Here is something else to consider. When you solve an equation like y^2=4, you want to find all solutions for y. That's why you need to consider both the square root of 4 and the opposite of the square root of 4. But, when you're given a square root expression, like √4, that expression refers to 2 (not -2). We call √4 the principal square root of 4. The opposite of √4 is written -√4, and that is -2.

#### Indranil

##### Junior Member
Because both 2^2 and (-2)^2 equal 4, and we're looking for all Real solutions.

Let's solve the equation y^2 = 4, by taking the square root of each side.

sqrt(y^2) = sqrt(4)

The square root of y^2 is not y; it is |y|. So the equation simplifies to:

|y| = 2

The rule for removing the absolute value symbols is to consider both roots.

y = ±2

Here is something else to consider. When you solve an equation like y^2=4, you want to find all solutions for y. That's why you need to consider both the square root of 4 and the opposite of the square root of 4. But, when you're given a square root expression, like √4, that expression refers to 2 (not -2). We call √4 the principal square root of 4. The opposite of √4 is written -√4, and that is -2.
Thanks a lot

#### tkhunny

##### Moderator
Staff member
If y^2 = 4, then why do we get two values +2 and -2 of 'y'?
y^2 = 4,
y = +2 and y = -2
This is why simply "taking the square root" is not particularly recommended.

y^2 = 4

y^2 - 4 = 0

(y+2)(y-2)=0

y = -2 or y = 2

It is much more clear why there are two correct solutions.

If you "take the square root", you must REMEMBER that there are two correct solutions.