How to know if a square root is rational or irrational?

Question

asked Aug 13, 2019 92.8k views

2 Answers

Luca Guarro · Answer 1 · 2019-08-16T05:03:51+0000

Hi!

If it can be written as a fraction, then it is rational. If it cannot, it is rational.

Here are some examples.

√4 = 2 = 2/1 = rational

√7 = 2.64575131... = irrational

Hope this helps! :)

-Peredhel

Supun Induwara · Answer 2 · 2019-08-19T20:03:06+0000

The square root of an integer is rational if the integer is a square. Otherwise, the root is irrational.

Example: √4 = √(2²) = 2, is rational. √3 is irrational.

_____

(It can be helpful to memorize the squares of small integers, up to about 20 or 25.)