what is the square root of 144
I am preparing for GRE and can anybody explain this to me
What is $\sqrt{144}$.
Why is the answer not $12 , -12. $
The calculator gives 12. does it mean -12 is incorrect?
$\endgroup$ 32 Answers
$\begingroup$While -12 is "a square root" of 144, the square root operation here denotes a function from nonnegative real numbers to nonnegative real numbers. A function can only produce a single result. So the expresion $\sqrt{144}$ evaluates to the positive root 12.
We refer to this convention by saying $\sqrt{x}$ is the principal square root of $x \ge 0$. See the Wikipedia article for more background.
$\endgroup$ $\begingroup$$144$ has two roots, yes: $\pm 12$. So $-12$ is a root of $144$.
However, we define the principal square root of $\sqrt {x^2} = |x|$, so in your case, $$\sqrt{144} = \sqrt{12^2} = |12| = 12$$
And your calculator is designed to return the principal square root. See Wolfram Alpha for the distinction: $12$ is the principal square root (what we mean by $\sqrt x$, given $x\geq 0$), and $-12$ is considered a real root.
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