Question

How do you simplify `sqrt(81x^4y^9z^2)`?

Answer 1

Find the squares under the root and take them out (un-squared)

`sqrt(81x^4y^9z^2)=sqrt(9^2*(x^2)^2*(y^4)^2*y*z^2)=`

`9x^2y^4zsqrty`

(the odd `y` remains under the root)

Answer 2

To the extent possible factor the argument of the square root into squares:

`sqrt(81x^4y^9z^2)`

`= sqrt(9^2*(x^2)^2*(y^4)^2*y*z^2)`

`= 9x^2y^4zsqrt(y)`

Answer 3

9`x^2` `y^4`z`sqrt(y)`

Except `y^9` all other terms are perfect squares, take square root of each of them and write outside the radical sign. Split `y^9` as y.`y^8`. Square root of `y^8` would be `y^4`. Write this outside the radical sign. The only term remaining inside the radical sign would be y. Hence the answer would be 9`x^2` `y^4`z`sqrty`