Question

How do you simplify `sqrt(54a^9)`?

Answer 1

`sqrt(54a^9) = 3a^4sqrt(6a)`
`color(white)("XXXX")`(of course, it is debatable whether this is really simpler).

Explanation:

Factoring `54a^9`
`color(white)("XXXX")` `54a^9 = (9*6)(a^8*a)`
`color(white)("XXXX")` `color(white)("XXXX")` `=(3^2*6)((a^4)^2*a)`
`color(white)("XXXX")` `color(white)("XXXX")` `=(3a^4)^2*(6a)`

`sqrt(54a^9)`
`color(white)("XXXX")` `=sqrt((3a^4)^2*(6a))`

`color(white)("XXXX")` `=sqrt((3a^4)^2) *sqrt(6a`

`color(white)("XXXX")` `=3a^4*sqrt(6a)`