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

1 Answer
Alan P.
Jul 24, 2015

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)

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