Question

How do you simplify Square root 18(5 square root 2 - square root 18)?

Answer 1

Probable intended answer: `36sqrt(2)`
It is possible to argue that the answer might be any of `+-36sqrt(2)` or `+-144sqrt(2)`

Explanation:

If "square root" is intended to mean only non-negative square root:

`sqrt(18) = sqrt(2*3^2) = sqrt(2)*3`

`18(5sqrt(2) - sqrt(18))`
`color(white)("XXXX")` `= 18( 5sqrt(2) - 3sqrt(2))`

`color(white)("XXXX")` `= 18(2sqrt(2))`

`color(white)("XXXX")` `=36sqrt(2)`

Alternate answers are possible if we interpret
`color(white)("XXXX")`"square root of 2" to mean `+-sqrt(2)`
and
`color(white)("XXXX")`"square root of 18" to mean `+-sqrt(18)`