Question

How do you simplify `sqrt192`?

Answer 1

`sqrt(192)=8sqrt(3)`

Explanation:

By observation,
or proceeding slowing by extracting smallest factors:
`192`
`color(white)("XXX")=2 * 96`
`color(white)("XXX")=2^2 * 48`
`color(white)("XXX")=2^2 * 2 * 24`
`color(white)("XXX")=2^2 * 2^2 * 12`
`color(white)("XXX")=2^2 * 2^2 * 2 * 6`
`color(white)("XXX")=2^2 * 2^2 * 2^2 * 3`
`color(white)("XXX")=(2^3)^2 * 3`
`color(white)("XXX")=8^2 * 3`

Therefore
`sqrt(192)=sqrt(8^2 * 3) = 8sqrt(3)`