# What is the Square root of 21?

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%.                                     <h4 class=answerHeader>Explanation:</h4>                                      <mathjax>%sqrt(21) = sqrt(3*7)%</mathjax> has no square factors that can be moved outside the square root sign. For example <mathjax>%sqrt(12) = sqrt(2^2*3) = sqrt(2^2)sqrt(3) = 2sqrt(3)%</mathjax>So <mathjax>%sqrt(21)%</mathjax> 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 <mathjax>%sqrt(21)%</mathjax> or give an approximation, such as <mathjax>%sqrt(21) ~~ 4. 58%</mathjax>.