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------------------------------------------------ What are the positive and negative square roots of [tex]$169$[/tex]?

Answer :

We want to find the numbers [tex]$x$[/tex] that satisfy

[tex]$$
x^2 = 169.
$$[/tex]

A number squared equals 169 if and only if [tex]$x$[/tex] is either positive or negative 13, because

[tex]$$
13^2 = 169 \quad \text{and} \quad (-13)^2 = 169.
$$[/tex]

Thus, we conclude:

- The positive square root of [tex]$169$[/tex] is [tex]$13$[/tex].
- The negative square root of [tex]$169$[/tex] is [tex]$-13$[/tex].

So the two numbers are [tex]$13$[/tex] and [tex]$-13$[/tex].