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### 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, $\sqrt{2}+\sqrt{18}=4\sqrt{2}$, which is another irrational number. However, $\sqrt{2}+\left(-\sqrt{2}\right)=0$, which is rational.
Likewise, the product of two irrational numbers is not always irrational. For example, $\sqrt{2}×\sqrt{2}=2$, which is rational.

## Want to join the conversation?

• what do you get if you sqrt a negative number?
• what ifit was a negitive
• Regardless of the sign, if it can be represented by a fraction then it's rational
• The sum of two irrational numbers is SOMETIMES irrational.
• Most of the time it is irrational unless they are additive inverses such as √3 + )-√3) = 0.
• So, if I'm correct, then when you multiply an irrational number by a rational number, you will never get an exact number because you can never find the value of the irrational number. If so, then when do we ever get irrational numbers and when do we actually need to use these in real life?
• When you use irrational numbers, such as pi, you usually round to a certain decimal place. _e_ is an interesting example of a common irrational number. It is found in spirals, like the head of a sunflower.
• irrational is a number that goes on forever like 3.14 rational is a number that can be turned into a fraction