How do you simplify #(5+4sqrt3)(3+sqrt3)#?

2 Answers
Apr 11, 2018

Answer:

Foil and combine like terms

Explanation:

Start by foiling. You should get #15+5sqrt3+12sqrt3+12#. If you're not sure how I got 12 it's because when you multiply roots they cancel so #sqrt3# times #sqrt3# became 3, and that 3 got multiplied by the 4 to become 12. Once you have #15+5sqrt3+12sqrt3+12#, you have to combine like terms so you get #17sqrt3+27#.

Apr 11, 2018

Answer:

#=17sqrt3+27#

Explanation:

Using the FOIL method, you can multiply the two terms together using the numbers inside each set of parenthesis.

#(5+4sqrt3)(3+sqrt3)#

F means "first terms."

#5*3=15#

I means "inner terms."

#4sqrt3*3=12sqrt3#

O means "outer terms."

#5*sqrt3=5sqrt3#

Finally, L means "last terms."

#4sqrt3*sqrt3=4*3=12#

Add your four results together and simplify to complete the foil.

#15+12sqrt3+5sqrt3+12#

#=17sqrt3+27#

That is the expanded form.