What is the Square root of 21?

1 Answer
Oct 17, 2015

Answer:

#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#.