This gives square and cubic radical expressions, but of complex numbers:
ToRadicals[RootReduce[ReIm[x /. Solve[x^7 == 1]]]]
What different result are you hoping to obtain?
I want to solve X^13==1
Perhaps Mr Rachida would like to reproduce some formulas in this page: Trigonometric constants expressed in real radicals.
To repeat, what result are you hoping to obtain?
please I want to solve X^13==1 , by radical expression
The result from Solve has, for example, (-1)^(2/13), which is a radical.
Solve
(-1)^(2/13)
This is not a radical expression for example:
Solve[X^3 == 1] {{X -> 1}, {X -> -(-1)^(1/3)}, {X -> (-1)^(2/3)}}
BUT,
ToRadicals[RootReduce[ReIm[X /. Solve[X^3 == 1]]]] {{1, 0}, {-(1/2), -(Sqrt[3]/2)}, {-(1/2), Sqrt[3]/2}}
I found another method to solve any equation X^n==1, by radical expression.