How do you simplify $sqrt(1215)$ ?

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Answer 1 · 2016-02-22T21:44:12

$9sqrt(15)$

First decompose 1215 in prime factors:

The last digit is 5 so it is multiple o f5:

$1215/5=243$

The sum of the digits of 243 its is 9, therefore it is multiple 3.

$243/3=81$ .

We know by the grammar school that $81=9xx9=3^4$ .

So $1215=3^5*5$

$Sqrt(1215)=sqrt(3^5*5)=sqrt(3^4*3*5)=3^2sqrt(3*5)=9sqrt(15)$

How do you simplify sqrt(1215)sqrt(1215)?