Who could have foreseen the veterinary consequences? Last week's Mercury News had the headline Balco questions dog shot putters Suppose you want to denest sqrt(2-sqrt(3)), i.e. the roots of (c174) x^2-(2-sqrt(3)) 2 (d174) x + sqrt(3) - 2 . A methodical approach, (modulo a little bird cheeping "sqrt(2)" in your ear): Clear the radicals by multiplying thru by their conjugates. (c175) expand(subst(-sqrt(3),sqrt(3),%)*%); 4 2 (d175) x - 4 x + 1 (Macsyma actually has a MULTIPLY_CONJUGATES.) Factor over the rationals extended by sqrt(2): (c176) algfac(%,sqrt(2)); 2 2 (d176) (x - sqrt(2) x - 1) (x + sqrt(2) x - 1) Now gcd the factors with the original polynomial: (c177) makelist(mygcd(d174,p),p,args(%)); (d177) [sqrt(2) x + sqrt(3) - 1, - sqrt(2) x + sqrt(3) - 1] (c178) map(linsolve,%); sqrt(2) sqrt(3) - sqrt(2) (d178) [[x = - -------------------------], 2 sqrt(2) sqrt(3) - sqrt(2) [x = -------------------------]] 2 These are the two square roots. --rwg