How do I know if a square root is irrational?
1 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!