The square root of 16 is 4. Why isn't it -4 ?   

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beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

If you write `sqrt(16)` this is equal to 4.   This is because the `sqrt(n)` without a sign in front signifies the principal square root which is always positive.   To signify both the positive and negative square roots we use `+-sqrt(16)` which is equal to both +4 and -4.  But when you ask in words what is the square root of 16 it is 4 or -4.  The reason for this is that `y=sqrt(x)` is a function, while `y=+-sqrt(x)` is not a function because one value of x gives two outputs.

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enotechris's profile pic

enotechris | College Teacher | (Level 2) Senior Educator

Posted on

Actually, it is!

The form for a square root (otherwise known as a radical) is

r^2 = x

which means that  the square root of x is a number r, which when multiplied by itself (r * r) yields x.

So in this case, 4^2 = (4 * 4) = 16, but also

(-4)^2 = (-4 * -4) = 16

So any positive real number, like 16, actually has 2 square roots, one positive, the other negative.  The positive square root is termed the "principal square root," the negative square root is unfortunately unnamed. So there's a bit of a misnomer; when you say "square root" it really refers to both negative and positive roots, but it has come to mean only the positive square root.

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