根式鏈
√2+√2+√2+√2+√2+...=2
√6+√6+√6+√6+√6+...=3
√12+√12+√12+√12+√12+...=4
√20+√20+√20+√20+√20+...=5
....
√a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+...=a，a是大於1的自然數.
假設x=√a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+...，則
x2=a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+√a(a−1)+...，
x2=a(a−1)+x，
(x−a)(x+a−1)=0，解得x=a。