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

Asked on by diya3ms

2 Answers | Add Yours

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.

Hope that helps...

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.

We’ve answered 319,863 questions. We can answer yours, too.

Ask a question