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

1 Answer
May 8, 2018

Answer:

#12+4sqrt5#

Explanation:

#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#