(3-2 square root 3)(3+2 square root 3)?

Question

947 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-20T04:46:46

-3

#(3-2sqrt3)(3+2sqrt3)#

foil:

#9 + 6sqrt3 - 6sqrt3 - 2sqrt3 * 2sqrt3#

#9 - 4*3#

#-3#

Answer 2 · 2018-05-20T04:48:12

#-3#

This is known as the difference of two squares.
#(a-b)(a+b) = a^2-b^2#

In this case, your #a=3# and your #b=2sqrt3#

So putting your two numbers into the formula,

you get #(3-2sqrt3)(3+2sqrt3) = 9-12 = -3#

You can also do this another way

#(3-2sqrt3)(3+2sqrt3) = 3(3+2sqrt3)-2sqrt3(3+2sqrt3) = 9+6sqrt3-6sqrt3-12 = 9-12 = -3#