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