What is the Square root of 20 - square root of 45 + 2 square root of 125?

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Answer 1 · 2015-09-19T14:17:01

#sqrt(20)-sqrt(45)+2sqrt(125) = 9sqrt(5)#

Use prime factorization to make it easier findthe perfect squares that can be taken out from the radical sign.

#sqrt(20)-sqrt(45)+2sqrt(125)# can be factorized to:

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

Then, take out the perfect squares and simplify them:

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

Finally, add the terms together to get the solution:

#2sqrt(5)-3sqrt(5)+10sqrt(5) = 9sqrt(5)#