Final answer:
In order to approximate the irrational number in the photo to the nearest 0.05, look at the digit in the hundredths place. If it is 5 or greater, round up, and if it is less than 5, round down.
Step-by-step explanation:
To approximate the irrational number in the photo to the nearest 0.05 without using a calculator, we need to look at the digit in the hundredths place. If the digit is 5 or greater, we round up, and if it is less than 5, we round down.
In this case, the digit in the hundredths place is 6, so we round up.
Therefore, the approximate value of the irrational number is 2,085.6.