Question 625623
{{{ i = sqrt(-1) }}}
{{{ sqrt(-54) = sqrt(-1)*sqrt(54) }}}
{{{ sqrt(-54) = sqrt(-1)*sqrt(9)*sqrt(6) }}}
{{{ sqrt(-54) = 3*sqrt(6)*i }}}
and also
{{{ sqrt(-54) = -3*sqrt(6)*i }}}
----------------------
To check, square both sides:
{{{ (sqrt(-54))^2 = (3*sqrt(6)*i)^2 }}}
{{{ -54 = 3^2*(sqrt(6))^2*i^2 }}}
{{{ -54 = 9*6*(-1) }}}
{{{ -54 = -54 }}}
OK
{{{ (sqrt(-54))^2 = (-3*sqrt(6)*i)^2 }}}
{{{ -54 = (-3)^2*(sqrt(6))^2*i^2 }}}
{{{ -54 = 9*6*(-1) }}}
{{{ -54 = -54 }}}
OK