<Dd> 1 a 3 + b 3 = a 2 3 − a b 3 + b 2 3 (a 3 + b 3) (a 2 3 − a b 3 + b 2 3) = a 2 3 − a b 3 + b 2 3 a + b . (\ displaystyle (\ frac (1) ((\ sqrt ((3)) (a)) + (\ sqrt ((3)) (b)))) = (\ frac ((\ sqrt ((3)) (a ^ (2))) - (\ sqrt ((3)) (ab)) + (\ sqrt ((3)) (b ^ (2)))) (\ left ((\ sqrt ((3)) (a)) + (\ sqrt ((3)) (b)) \ right) \ left ((\ sqrt ((3)) (a ^ (2))) - (\ sqrt ((3)) (ab)) + (\ sqrt ((3)) (b ^ (2))) \ right))) = (\ frac ((\ sqrt ((3)) (a ^ (2))) - (\ sqrt ((3)) (ab)) + (\ sqrt ((3)) (b ^ (2)))) (a + b)) \, .) </Dd> <P> Simplifying radical expressions involving nested radicals can be quite difficult . It is not obvious for instance that: </P> <Dl> <Dd> 3 + 2 2 = 1 + 2 (\ displaystyle (\ sqrt (3 + 2 (\ sqrt (2)))) = 1 + (\ sqrt (2))) </Dd> </Dl> <Dd> 3 + 2 2 = 1 + 2 (\ displaystyle (\ sqrt (3 + 2 (\ sqrt (2)))) = 1 + (\ sqrt (2))) </Dd>

What value is the nth root of unity for any value n