Question

How do you simplify `sqrt(54)`?

Answer 1

`sqrt(54) = 3sqrt(6)`

Explanation:

Factor `54` into primes:
`color(white)("XXXX")` `54=2*27`
`color(white)("XXXX")` `=2*3*9`
`color(white)("XXXX")` `=2*3*3*3`

Grouping pairs of identical factors:
`color(white)("XXXX")` `54 = 3^2*3*2`
`color(white)("XXXX")` `=3^2*6`

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

`color(white)("XXXX")` `=3sqrt(6)`