Question

How do you simplify `\sqrt{\frac{122x^{8}}{25y^{4}}}`?

Answer 1

`sqrt((122x^8)/(25y^4))=color(green)((sqrt(122)x^4)/(5y^2))`

Explanation:

`color(red)(122x^8= 122 * (x^4)^2)`
`color(red)(sqrt(122x^8) =sqrt(122) * sqrt((x^4)^2)=sqrt(122)x^4)`

`color(blue)(25y^4=5^2 * (y^2)^2)`
`color(blue)(sqrt(25y^4)= sqrt(5^2) * sqrt((y^2)^2)=5y^2)`

`sqrt((122x^8)/(25y^4))=color(red)(sqrt(122x^8))/color(blue)(sqrt(25y^4))= color(red)(sqrt(122)x^4)/color(blue)(5y^2)`