Yes the number 8.25635..., is an irrational number.
An irrational number is any number that cannot be written as a whole number or a simple fraction. When the result of a mathematical calculation results in non-stop decimals, (like the one in your question), you cannot possibly convert it into a fraction, and that makes it irrational.
Every whole number or fraction that that can be easily converted into a decimal is a rational number. For example, 1/5 is a rational number because it can be written as 0.2. However 1/6 is an irrational number is because the result is 0.6666..., and it has no end. It keeps recurring.