# How to check if a square root is irrational

What's the easiest way in sage to check if the square root of a given rational number (for example 1,671 or 2,56) is irrational.

How to check if a square root is irrational

**
asked 2012-10-13 11:00:30 +0200 **

Anonymous

What's the easiest way in sage to check if the square root of a given rational number (for example 1,671 or 2,56) is irrational.

add a comment

2

Convert your numbers to explicit rationals and ask whether their square root is in **Q**:

```
sage: sqrt(1671/1000) in QQ
False
sage: sqrt(256/100) in QQ
True
sage: sqrt(2) in QQ
False
```

Or you can do the conversions this way:

```
sage: sqrt(QQ(1.671)) in QQ
False
```

Please start posting anonymously - your entry will be published after you log in or create a new account.

Asked: ** 2012-10-13 11:00:30 +0200 **

Seen: **1,999 times**

Last updated: **Oct 13 '12**

Counting number of trues in a 1000 line answer

check if the result is a real number

Why is 3e1 not equivalent to 30?

Converting string into number does not work properly

What are the different real numbers in Sage ?

What are the differences between RealDoubleField() and RealField(53) ?

Get Sage to display the 2nd x value, when function is set to 0?

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.