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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