How do you simplify: square root of x^6*y^6?

1 Answer
Aug 2, 2015

Answer:

Divide the exponent by 2 and this will be the number of variables you can extract from the root.

Explanation:

If you got #sqrt(x^6y^6)#, divide each exponent by the index of the root (in this case, a square root has index 2), we obtain #6/2=3#
So we can extract each variable 3 times. You can see it more graphically this way:

#sqrt(x^6y^6)=sqrt(x^2x^2x^2y^2y^2y^2)=x^3y^3#