The sum of two irrational numbers is SOMETIMES irrational." The sum of two irrational numbers, in some cases, will beirrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational

**Yes**, the sum of two irrational numbers may be either a rational number or an irrational number. To understand this, we need to first define what irrational numbers and rational numbers are.

**Rational Numbers:**
Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. For example, 1/2, 3/4, and -5/7 are all rational numbers.

**Irrational Numbers:**
Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Their decimal representations are non-terminating and non-repeating. Examples of irrational numbers include √2, π (pi), and e (Euler's number).

**Sum of Two Rational Numbers:**
If we take the sum of two rational numbers, the result will always be a rational number. This is because the sum of two fractions can be expressed as a fraction itself. For example, if we add 1/2 and 3/4, we get 5/4, which is a rational number.

**Sum of Two Irrational Numbers:**
When we add two irrational numbers, the result can be either rational or irrational. It depends on the specific numbers being added.

**Example 1:**
If we add √2 and √2, we get 2√2. This number cannot be expressed as a fraction, and its decimal representation is non-terminating and non-repeating. Therefore, the sum of these two irrational numbers is also an irrational number.

**Example 2:**
On the other hand, if we add √2 and -√2, the result is 0. This is a rational number because it can be expressed as the fraction 0/1.

**Conclusion:**
In conclusion, the sum of two irrational numbers can be either a rational or an irrational number. It depends on the specific numbers being added.