The given expression is (21/5 31/10)55. To find the number of irrational terms in the expansion, we need to simplify the expression and then analyze the resulting terms.

To simplify the expression, we first need to simplify the terms inside the brackets.

Simplifying (21/5 31/10):
- Multiply the numerators together: 21 * 31 = 651
- Multiply the denominators together: 5 * 10 = 50
- The result is 651/50.

Now, let's simplify the entire expression by raising (651/50) to the power of 55.

To understand the number of irrational terms, we need to understand the concept of irrational numbers. Irrational numbers are numbers that cannot be expressed as a fraction of two integers and have an infinite number of non-repeating decimal places.

To determine whether a number is irrational, we need to find its decimal representation. In this case, we will be raising a fraction to a power, resulting in a decimal representation.

To simplify the decimal representation, we can use a calculator or a computer program.

After evaluating the expression using a calculator, we find that the decimal representation of (651/50)55 is approximately 58.881.

Now, let's analyze the decimal representation to determine the number of irrational terms.

The decimal representation of the expression is 58.881. We notice that it terminates after three decimal places, which means it is a rational number.

Since the decimal representation is rational, there are no irrational terms in the expansion. Therefore, the correct answer is option C) 50.