Simplify the following:
sqrt(6 sqrt(5) + 14)
Factor 2 out of 14 + 6 sqrt(5) giving 2 (3 sqrt(5) + 7):
sqrt(2 (3 sqrt(5) + 7))
2 (7 + 3 sqrt(5)) = 9 + 6 sqrt(5) + 5 = 9 + 6 sqrt(5) + (sqrt(5))^2 = (sqrt(5) + 3)^2:
sqrt((sqrt(5) + 3)^2)
Cancel exponents. sqrt((3 + sqrt(5))^2) = sqrt(5) + 3:
3 + sqrt(5)
