# How do I know if a square root is irrational?

##### 1 Answer

#### Answer:

See below:

#### Explanation:

Let's say we have

This is irrational if

When we simplify radicals, we try to factor out perfect squares. For example, if we had

We know that

We know that

Remember what irrational means- we cannot express the number as a ratio of two other numbers.

We know that the principal root of

We have expressed

For a much better explanation on why the square root of a prime number is irrational, I strongly encourage you to check out this Khan Academy video.

Hope this helps!