This is an equation of the fourth degree, so it has four roots (solutions) -- two real and two complex. The real roots are +(27)^(1/4) and -(27)^(1/4), i.e. plus or minus the fourth real root of 27. To see the other answers, let b = 27^(1/4) and write the given equation as x^4 - b^4 = 0. Recognize this as the difference of two squares so it factors as (x2 - b2)(x2 + b2).





Again, the first factor is the difference of two squares and it factors as (x2 - b2)= (x+b)(x-b). Setting each of these linear factors equal to 0 gives the (real) answers we already noted. Using complex factorization, the second expression also factors as (x2 + b2) = (x + bi)(x - bi) where i2 = -1. Setting each of these factors = 0 gives the complex solutions bi and -bi, where b is the fourth root of 27.

x^4 -27 = 0

x^4 = 27

root^4 of 27 = x

It will be between 2 and 3.

x^4=27



x=sqrt(sqrt(27))=2.2795

it would be sqrt(sqrt(27))



+2.27 or -2.27