The sum of a rational number and irrational number is always an irrational number.

Yes, the statement is correct. The sum of a rational number and an irrational number is always an irrational number. Here's why:

Step 1: Understand the terms. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. An irrational number cannot be expressed as a ratio between two numbers and it does not repeat or terminate.

Step 2: Consider an example. Let's take a rational number, say 2, and an irrational number, say √2.

Step 3: Add the two numbers. 2 + √2 = 2.41421356... The result is a non-repeating, non-terminating decimal, which is the definition of an irrational number.

Therefore, the sum of a rational number and an irrational number is always an irrational number.