How do you simplify #5\sqrt { 125} + 3\sqrt { 45} - 8\sqrt { 20}#?

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Answer 1 · 2017-11-13T03:55:53

See a solution process below:

First, rewrite the radicals as:

#5sqrt(25 * 5) + 3sqrt(9 * 5) - 8sqrt(4 * 5)#

Then use this rule of radicals to simplify the radicals:

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

#5sqrt(25)sqrt(5) + 3sqrt(9)sqrt(5) - 8sqrt(4)sqrt(5) =>#

#(5 * 5)sqrt(5) + (3 * 3)sqrt(5) - (8 * 2)sqrt(5) =>#

#25sqrt(5) + 9sqrt(5) - 16sqrt(5)#

Now, we can factor out the common term to complete the simplification:

#(25 + 9 - 16)sqrt(5) =>#

#18sqrt(5)#