How do you simplify 2√3 - 4√3 + 7√2?

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Answer 1 · 2018-02-23T00:34:48

#-2sqrt3+7sqrt2# or #7sqrt2-2sqrt3#

We let:
#x=sqrt3#
#y=sqrt2#

We replace our square roots with these variables.

#2sqrt3-4sqrt3+7sqrt2=>2x-4x+7y#

Now, we can combine like terms.
#2x-4x+7y# since #2# and #4# are being multiplied by #x#, we subtract these two numbers.

We now have:

#(2-4)x+7y#

#=>-2x+7y#

If you want the first term to be positive, then:

#=>+(-2x)+7y# Using the commutative property of addition,

#=>7y+(-2x)#

#=>7y-2x#

We now substitute #x# and #y# with #sqrt3# and #sqrt2#

#-2sqrt3+7sqrt2# or #7sqrt2-2sqrt3#