How do you simplify #(4-sqrt3)(12+5sqrt3)#?

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Answer 1 · 2016-02-07T02:52:16

#33+8sqrt3#

Begin by expanding the brackets. By doing this we get:

#4*12+4*5sqrt3-sqrt3*12-sqrt3*5sqrt3#

Now if we do the multiplications we get:

#48 +20sqrt3-12sqrt3-15#

We can now simplify by gathering the like terms:

#33+8sqrt3#

Answer 2 · 2016-02-07T02:57:43

Multiply everything with everything.

#(4 - sqrt(3))(12 + 5sqrt(3))#

= #48 - 12sqrt(3) + 20sqrt(3) - 5sqrt(9)#

= #48 - 15 + 8sqrt(3)#

= #33 + 8sqrt(3)#

Practice exercises:

a) #(3 - 2sqrt(5))(4 + sqrt(10))#

b) #(4sqrt(6) + 5sqrt(11))(3sqrt(7) - 9)#

c) #(2 + sqrt(13))(2 - sqrt(13))#

d) #(sqrt(2) - sqrt(15))^2#