How do you simplify #2(sqrt3)-4(sqrt2)+6(sqrt3)+8(sqrt2)#?

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Answer 1 · 2017-05-29T14:40:40

See a solution below:

First, group like terms. In this problem the like terms are the radicals:

#2(sqrt(3)) + 6(sqrt(3)) - 4(sqrt(2)) + 8(sqrt(2))#

Next, factor the common terms:

#(2 + 6)(sqrt(3)) + (-4 + 8)(sqrt(2))#

#8(sqrt(3)) + 4(sqrt(2))#

Now, factor out the common term outside the radical:

#(4 xx 2)(sqrt(3)) + 4(sqrt(2))#

#4(2(sqrt(3)) + (sqrt(2)))#

#4(2sqrt(3) + sqrt(2))#

Answer 2 · 2017-05-29T14:40:45

#color(green)(4(sqrt2+2sqrt3)#

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

#:.=2sqrt3+6sqrt3-4sqrt2+8sqrt2#

#:.=8sqrt3+4sqrt2#

#:.=color(green)(4(sqrt2+2sqrt3)#

check:

#:.color(green)(2(sqrt3)-4(sqrt2)+6(sqrt3)+8(sqrt2)=19.51326071#

#:.color(green)(4(sqrt2+2sqrt3)=19.51326071#