How do you simplify #2 sqrt 3 - 4 sqrt 2 + 6 sqrt3 + 8 sqrt 2#?

1 Answer

Answer:

Combine like terms and factor to get to #4sqrt2(sqrt6+1)#

Explanation:

We can combine like terms, so the terms with #sqrt3# in them can be combined and those with #sqrt2# can be combined, like this:

#2sqrt3-4sqrt2+6sqrt3+8sqrt2#

#2sqrt3+6sqrt3+8sqrt2-4sqrt2#

#8sqrt3+4sqrt2#

We can then factor out a 4 from each term, to get:

#4(2sqrt3+sqrt2)#

We can also write #2sqrt3# as:

#4(sqrt2sqrt2sqrt3+sqrt2)#

so we can factor out another #sqrt2#:

#4sqrt2(sqrt6+1)#