The

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

So, adding two rationals is the

**same**as adding two such fractions, which will result in another fraction of this**same**form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.What is a rational and irrational number?

A

**rational number**is part of a whole expressed as a fraction, decimal or a percentage. It is a**number**that cannot be written as a ratio of two integers (or cannot be expressed as a fraction). For**example**, the square root of 2 is an**irrational number**because it cannot be written as a ratio of two integers.Is the product of a rational and irrational number rational?

"The

**product**of a non-zero**rational number**and an**irrational number**is**irrational**." Indirect Proof (Proof by Contradiction) of the better statement: (Assume the opposite of what you want to prove, and show it leads to a contradiction of a known fact.)