Find the first digit before and after the decimal point in the base ten expansion of (√2 + √3)²⁰¹¹.

For an extra challenge, solve this puzzle without using a computer program.

(In reply to The Broll guesses... by broll)

Why did you stop at  (a+b)^2000?
Your reasoning breaks down if you instead use a different large even power:

= (a+b)^2002*(a+b)^9

=(something huge)+0.9999999999........9*(a+b)^9

(a+b)^9= 30210.4301525

so the digits before and after the decimal point should be ...0.4...?

Posted by Jer on 2011-03-25 14:28:25