Question

What is the Square root of 21?

Answer 1

`21 = 3*7` has no square factors, so `sqrt(21)` cannot be simplified.

`sqrt(21) ~~ 4.58257569495584000658` is an irrational number whose square is `21`.

Explanation:

`sqrt(21) = sqrt(3*7)` has no square factors that can be 'moved outside the square root sign'.

For example `sqrt(12) = sqrt(2^2*3) = sqrt(2^2)sqrt(3) = 2sqrt(3)`

So `sqrt(21)` cannot be simplified.

It cannot be expressed as a rational number (fraction), so the best we can do with normal notation is to either stick with `sqrt(21)` or give an approximation, such as `sqrt(21) ~~ 4.58`.