How do you simplify # 32div(6-2sqrt5)#?

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Answer 1 · 2018-05-08T09:33:15

#12+4sqrt5#

#32÷(6-2sqrt5)#

means

#32/(6-2sqrt5)#

multiply by the conjugate

#32/(6-2sqrt5)*(6+2sqrt5)/(6+2sqrt5)#

#color(red)((6-2sqrt5)*(6+2sqrt5) = 6^2 - (2sqrt5)^2=36-20 = 16)#

#color(red)("difference of two sequares")#

#(32*(6+2sqrt5))/ 16#

#color(red)(32/16 = 2)#

#2*(6+2sqrt5) = 12+4sqrt5#