Question

Hey guys,

See, 2nd root of 4 is Square root of 4, i.e, 2
3rd root of 27 is cube root of 27 , i.e., 3

Similarly, 10th root of 1024 is 2;

Now, The question for Calculator users, what is :-
-------> 10^9th root of 2 or say:-

What is 1000000000th root of 2 ?

Answer 1

For very large powers and roots we can do like this.

Q1)   Let  y be a small real number.  y << 1.

       10⁹ th root of 2 = 1 + y  (say).
       1000,000,000 th root of 2 = 1 + y
       (1 + y)¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 2
As y << 1,
        1 + 1000,000,000 y = 2
        y = 10⁻⁹       
Answer :    $\sqrt[1000000000]{2}=1.000000001$

     answer:  1.000000001 = 1 + (2 - 1)* 10⁻⁹