How do you evaluate #5\sqrt { 8} - 2\sqrt { 27} + 2\sqrt { 75} - 3\sqrt { 18}#?

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Answer 1 · 2017-12-09T02:12:27

See a solution process below:

First, rewrite each of the radicals as:

#5sqrt(4 * 2) - 2sqrt(9 * 3) + 2sqrt(25 * 3) - 3sqrt(9 * 2)#

Next, use this rule of radicals to simplify each radical term:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#5sqrt(4)sqrt(2) - 2sqrt(9)sqrt(3) + 2sqrt(25)sqrt(3) - 3sqrt(9)sqrt(2) =>#

#(5 * 2)sqrt(2) - (2 * 3)sqrt(3) + (2 * 5)sqrt(3) - (3 * 3)sqrt(2) =>#

#10sqrt(2) - 6sqrt(3) + 10sqrt(3) - 9sqrt(2)#

Then, combine like terms (the radicals):

#10sqrt(2) - 9sqrt(2) - 6sqrt(3) + 10sqrt(3)#

Now, combine like terms:

#(10 - 9)sqrt(2) + (-6 + 10)sqrt(3) =>#

#1sqrt(2) + 4sqrt(3) =>#

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