let x=(1000000000000000000001)^{20} then, under root x^{2}+x is equal to what?

Try the rule for adding exponents when multiplying terms:

x=(1000000000000000000001)^20

x^2+x =[(1000000000000000000001)^20]*[(1000000000000000000001)^20] +

(1000000000000000000001)^20

= {(1000000000000000000001)^40} + (1000000000000000000001)^20

Don't let all the zeros baffle you.

*BruceS*