How do you simplify #20sqrt10+12+(-75sqrt2)-9sqrt5 #?

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Answer 1 · 2015-10-08T23:52:28

#3 * (4 - 3sqrt(5)) + 5sqrt(2) * (4sqrt(5) - 15)#

Your starting expression looks like this

#20sqrt(10) + 12 -75sqrt(2) - 9sqrt(5)#

Right from the start, you can say that #12#, the only term that doesn't have a radical attached, will remain by itself.

As far as the other terms are concerned, you don't really have that much elbow room. You could try to write #10 = 2 * 5# and get

#20sqrt(10) = 20sqrt(2 * 5) = 20 * sqrt(2) * sqrt(5)#

Now you could use #5sqrt(2)# as a common factor to write

#12 + 5sqrt(2) * (4sqrt(5) - 15) - 9sqrt(5)#

Now you could maybe use #3# as a common factor between #12# and #9sqrt(5)# to get

#3 * (4 - 3sqrt(5)) + 5sqrt(2) * (4sqrt(5) - 15)#

And that's about it.