Convention

denotes the non-negative root

Algebra • Surds

Formula

x^{2} = ∣ x ∣

For

x \geq 0

x

denotes the non-negative root only. Hence

x^{2} = ∣ x ∣

, not

x

. The equation

x^{2} = 9

has two solutions

x = \pm 3

, but

9 = 3

alone.

How to use it

1Distinguish solving $x^{2} = k$ (two roots) from evaluating $k$ (one value).
2When a length or a magnitude is asked for, the negative root is discarded on physical grounds, not by this convention.

Evaluate

(- 5)^{2}

Step-by-step

1
$(- 5)^{2} = 25 = 5$
Why: The radical returns the non-negative root, so the answer is $∣ - 5∣$ .

Answer

5

Watch out

A frequent distractor is

- 5

, obtained by cancelling the square with the root.

Also known as

principal square root, positive root convention