# 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

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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.

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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
```

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

Seen: **1,513 times**

Last updated: **Oct 13 '12**

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