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# Simplify an expression of square roots

Sage's .simplify() command is unable to simplify the expression $\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6}$: the output of both

(sqrt(6) * sqrt(3) * sqrt(2)).simplify()

and

(sqrt(6) * sqrt(3) * sqrt(2)).simplify_full()

is just sqrt(6)sqrt(3)sqrt(2) again.

Notably, (sqrt(6)sqrt(3)sqrt(2)).is_integer() also returns false.

Is there a more powerful version of the simplify command that won't get overwhelmed by an expression like this?

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## 1 Answer

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You can do:

sage: a = sqrt(6) * sqrt(3) * sqrt(2)
sage: a.canonicalize_radical()
6


canonicalize_radical is not parrt of the full_simplify method, IIRC because of some monodromy issues (winding around singularities in the complex plane does not commute with chosing a single branch of a multi-valued function), canonicalize_radical is not parrt of the full_simplify method anymore.

Here, since everything is assumed to be real, there is no real issue.

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## Comments

That's exactly what I need, thanks!

( 2016-10-23 22:16:21 +0200 )edit

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Asked: 2016-10-23 20:31:31 +0200

Seen: 1,060 times

Last updated: Oct 23 '16