Question

How do you simplify `\sqrt { 12x ^ { 4} y ^ { 2} z ^ { 2} }`?

Answer 1

`sqrt(12x^(4)y^(2)z^(2))=color(blue)(2sqrt3x^2yz`

For the process refer to the explanation.

Explanation:

Simplify:

`sqrt(12x^(4)y^(2)z^(2))`

Apply the square root rule: `sqrt(ab)=sqrtasqrtb`.

`sqrt(12)sqrt(x^4)sqrt(y^2)sqrt(z^2)`

Determine `sqrt(12)` by prime factorization.

`sqrt(color(red)(2xx2)xxcolor(blue)3)sqrt(x^4)sqrt(y^2)sqrt(z^2)`

`color(red)2sqrtcolor(blue)3sqrt(x^4)sqrt(y^2)sqrt(z^2)`

Simplify `sqrt(x^4)` to `x^2`.

`color(red)2sqrtcolor(blue)3color(green)(x^2)sqrt(y^2)sqrt(z^2)`

Simplify `sqrt(y^2)` to `y`.

`color(red)2sqrtcolor(blue)3color(green)(x^2)color(purple)ysqrt(z^2)`

Simplify `sqrt(z^2)` to `z`.

`color(red)2sqrtcolor(blue)3color(green)(x^2)color(purple)ycolor(magenta)z`