Question

What are all square roots of `100/9`?

Answer 1

`10/3 and -10/3`

Explanation:

First, noting that

`sqrt(100/9) = sqrt(100)/sqrt(9)`

It is noted that the numbers on the top of the fraction (the numerator) and the bottom of the fraction (the denominator) are both "nice" square numbers, for which it is easy to find roots (as you will certainly know, `10` and `9`, respectively!).

What the question is really testing (and the clue for that is provided by the word "all") is whether you know that a number will always have two square roots.

That is the square root of `x^2` is
plus or minus `x`

Confusingly, by convention (at least sometimes, for example in the standard way of expressing the quadratic formula) the square root sign is used to denote only the positive root. If in doubt, you could use the alternative way of showing a square root, which is a number raised to the power of one half ie

`x^(1/2) = +- sqrt(x)`