How do you simplify 5 square root 6 minus 4 square root 10 minus square root 6 plus 12 square root 10?

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Answer 1 · 2015-09-09T20:24:06

#4 * (sqrt(6) + 2sqrt(10))#

Your starting expression (probably) looks like this

#5sqrt(6) - 4sqrt(10) - sqrt(6) + 12sqrt(10)#

You can regroup the like-terms to get

#5sqrt(6) - sqrt(6) - 4sqrt(10) + 12sqrt(10)#

Now you can factorize like-terms to get

#sqrt(6) * (5 - 1) + sqrt(10) * (12 - 4)#

#4sqrt(6) + 8 sqrt(10)#

All you can do now is factor this expression

#4sqrt(6) + 4 * 2 * sqrt(10) = color(green)(4 * (sqrt(6) + 2sqrt(10)))#