How do you multiply #(sqrt3+ 2sqrt5)^2#?

1 Answer
Alan P.
Jul 5, 2015

#(sqrt(3)+2sqrt(5))^2#
#color(white)("XXXX")#

Explanation:

#(sqrt(3)+2sqrt(5))^2#
#color(white)("XXXX")##=color(red)((sqrt(3)+2sqrt(5)))*color(blue)((sqrt(3)+2sqrt(5)))#

#color(white)("XXXX")##=color(red)((sqrt(3)+2sqrt(5)))*color(blue)((sqrt(3)))+color(red)((sqrt(3)+2sqrt(5)))*color(blue)((2sqrt(5))#

#color(white)("XXXX")##= color(red)((sqrt(3)))*color(blue)((sqrt(3))) +color(red)((2sqrt(5))*color(blue)((sqrt(3)))+color(red)((sqrt(3))*color(blue)((2sqrt(5)))+color(red)((2sqrt(5)))*color(blue)((2sqrt(5)))#

#color(white)("XXXX")##= 3 + 2sqrt(15) + 2sqrt(15) + 20#

#color(white)("XXXX")##=23 + 4sqrt(15)#

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