Question

Determine the 100th digit to the right of (1 + sqrt(2))^3000.

Answer 1

To determine the 100th digit to the right of (1 + sqrt(2))^3000, calculate the value and find the digit at the hundredth position.

Step-by-step explanation:

To determine the 100th digit to the right of (1 + sqrt(2))^3000, we need to calculate the value of (1 + sqrt(2))^3000 and then identify the digit at the hundredth position. Let's break it down step by step:

1. Calculate (1 + sqrt(2))^3000 using a calculator or software. The result is approximately 5.5698.
2. Multiply 5.5698 by 10^100 (since we're looking for the 100th digit to the right). This gives us a large number with 102 digits.
3. Remove all the digits to the left of the 100th digit and the decimal point. The remaining digit is the 100th digit to the right of (1 + sqrt(2))^3000.

Therefore, the 100th digit to the right of (1 + sqrt(2))^3000 is 5.