Question

How do you simplify `sqrt(162x^6)/sqrt(64x^2)`?

Answer 1

`(sqrt(162x^6))/(sqrt(64x^2))= 9/8 x sqrt(2)`

Explanation:

Factoring `162x^6`
`color(white)("XXXX")` `= 2xx(81) xx (x^3)^2`
`color(white)("XXXX")` `= 2xx (9x^3)^2`

`sqrt(162x^6)`
`color(white)("XXXX")` `=sqrt(2xx(9x^3)^2)`
`color(white)("XXXX")` `=9x^3sqrt(2)`

Factoring `64x^2`
`color(white)("XXXX")` `=(8x)^2`

`sqrt(64x^2)`
`color(white)("XXXX")` `=sqrt((8x)^2)`
`color(white)("XXXX")` `=8x`

`(sqrt(162x^6))/(sqrt(64x^2)`
`color(white)("XXXX")` `= (9x^3sqrt(2))/(8x)`

`color(white)("XXXX")` `= 9/8 x^2 sqrt(2)`