What is #-sqrt(20) + 3 sqrt(45)#?

1 Answer
YC
Jan 22, 2017

#7sqrt(5)#

Explanation:

  1. Factor the numbers under each square root and look for "perfect square" factors
    #-sqrt(color(red)((4)(5))) + 3sqrt(color(red)((9)(5)))#

  2. Separate the terms in the square roots
    #-color(red)(sqrt(4)sqrt(5))+3color(red)(sqrt(9)sqrt(5))#

  3. Simplify the roots (#sqrt(4)=2# and #sqrt(9)=3#)
    #-color(red)(2)sqrt(5)+3color(red)((3))sqrt(5)#

  4. Simplify
    #-2sqrt(5)+color(red)(9)sqrt(5)#

  5. Combine terms
    #7sqrt(5)#

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