# what does '3*sqrt(3)' means?

I am confused in reading some results of software. Please explain me what the statement means. In the screen shot what is '3*sqrt(3)' means? and why it doesn't appears with decimal values integers?

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sqrt stands for "square root", so 3*sqrt(3) means $3\sqrt{3}$.

Now, if you want a numerical representation of your number, you can use the .n() method:

sage: a = 3*sqrt(3)
sage: a.n()
5.19615242270663

more

I want to know that how can sqrt(27) can be 3*sqrt(3). I know that I can get the decimal value by using .n() or .numerical_approx() but I want to know that what does that statement really mean? and how it is useful for a user?, I mean it should directly shown the value given by .numerical_approx() function.

I am very thankful that you replied to my question. Actually I am starting contributing to sage so it is necessary to understand each and every output.

It would be great if you help me a bit more.

( 2016-10-03 12:25:09 -0500 )edit

27 is equal to 3^2*3, so sqrt(27) is simplified to 3*sqrt(3) (here, simplifying means having as less as possible under the sqrt symbol).

( 2016-10-03 16:52:46 -0500 )edit

Thank you so much. Now I got know that what I was missing. I appreciate your concern.

( 2016-10-04 11:37:21 -0500 )edit

^_^ .

( 2016-10-04 12:12:38 -0500 )edit

@tmonteil, this seems weird. Why should Meth:sqrt return a simplified expression instead of the direct numerical value in some cases and not others? For instance, sqrt(6.1) gives 2. something directly, while I have to do n(sqrt(27)) to get 5. I get that this can be simplified and so it is, but why should that be its native behaviour instead of the decimal value? Also, is this a native Sage method or does it belong to some other package?

( 2016-10-04 12:21:12 -0500 )edit