How do you simplify #sqrt100 - sqrt130 + sqrt130 - sqrt169#?

1 Answer
Sep 19, 2015

Answer:

#sqrt(100) - sqrt(130) + sqrt(130) - sqrt(169) = -3#

Explanation:

The two middle terms, #- sqrt(130)# and #sqrt(130)#, cancel each other out and can be removed.

Use prime factorization to find and simplify the perfect squares:

#sqrt(100) - sqrt(169) = sqrt(5*5*2*2) - sqrt(13*13) = sqrt(5^2)sqrt(2^2) - sqrt(13^2) = 5*2 - 13 = -3#