# 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 04:00:30 -0600
**

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.

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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
```

Asked: **
2012-10-13 04:00:30 -0600
**

Seen: **1,420 times**

Last updated: **Oct 13 '12**

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