What is the Square root of 21?

##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##.

##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##.