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

1 Answer
May 8, 2018

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