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## Algebra 1

### Course: Algebra 1>Unit 15

Lesson 3: Proofs concerning irrational numbers

# Irrational numbers: FAQ

## What is an irrational number?

An irrational number is a real number that cannot be written as a ratio of two integers. In other words, it can't be written as a fraction where the numerator and denominator are both integers. Irrational numbers often show up as non-terminating, non-repeating decimals.

## Where do irrational numbers come up in the real world?

Irrational numbers show up all over the place! For example, the number pi is irrational and it's key for working with circles. The square root of 2, another irrational number, is important for understanding right triangles.

## How can we tell if a number is rational or irrational?

If we can write the number as a fraction of two integers, then it's rational. Otherwise, it's irrational.

## Are there any rules for adding or multiplying rational and irrational numbers?

Yes! When we add or multiply two rational numbers, we'll always get a rational number as the result. But when we add or multiply a rational number with an irrational number, we'll end up with an irrational number.

## What do we know about the sum and product of two irrational numbers?

There are a few things to keep in mind. For one, the sum of two irrational numbers is not always irrational. For example, square root of, 2, end square root, plus, square root of, 18, end square root, equals, 4, square root of, 2, end square root, which is another irrational number. However, square root of, 2, end square root, plus, left parenthesis, minus, square root of, 2, end square root, right parenthesis, equals, 0, which is rational.
Likewise, the product of two irrational numbers is not always irrational. For example, square root of, 2, end square root, times, square root of, 2, end square root, equals, 2, which is rational.