Question 175900
{{{sqrt(27c^5*d^10*e^9)}}} Start with the given expression.



{{{sqrt(27c^4*c*d^10*e^8*e)}}} Factor {{{c^5}}} to get {{{c^4*c}}}. Factor {{{c^5}}} to get {{{e^8*e}}}.



{{{sqrt(27)*sqrt(c^4)*sqrt(c)*sqrt(d^10)*sqrt(e^8)*sqrt(e)}}} Break up the square root.



{{{3*sqrt(3)*sqrt(c^4)*sqrt(c)*sqrt(d^10)*sqrt(e^8)*sqrt(e)}}} Simplify {{{sqrt(27)}}} to get {{{3*sqrt(3)}}}



{{{3*sqrt(3)*c^2*sqrt(c)*sqrt(d^10)*sqrt(e^8)*sqrt(e)}}} Take the square root of {{{c^4}}} to get {{{c^2}}} (notice how the exponent is cut it in half)



{{{3*sqrt(3)*c^2*sqrt(c)*d^5*sqrt(e^8)*sqrt(e)}}} Take the square root of {{{d^10}}} to get {{{d^5}}} (notice how the exponent is cut it in half)



{{{3*sqrt(3)*c^2*sqrt(c)*d^5*e^4*sqrt(e)}}} Take the square root of {{{e^8}}} to get {{{e^4}}} (notice how the exponent is cut it in half)




{{{3c^2*d^5*e^4*sqrt(3ce)}}} Recombine the radicals.



So {{{sqrt(27c^5*d^10*e^9)}}} simplifies to {{{3c^2*d^5*e^4*sqrt(3ce)}}}