SOLUTION: Simplify cube root of (2 + √5)

We seek to find a simpler form } 

We try to find a simpler expression of the same form as what's 
under the radical, namely a surd of the form , where 
a and b are rational numbers.

If this is possible, then



Cubing both sides:









The rational terms on the left must equal the rational terms on the right,
and The irrational terms on the left must equal the irrational terms on the
right, so we have this system



Eliminate the constants by multiplying the 2nd equation by -2



Adding the equations:



Notice that the coefficients have sum 1-6+15-10 = 0.

That means a=b is a solution. Substituting a for b,











Taking cube roots of both sides:



and since a=b, 



becomes



Edwin