Simplify the expression. Write your answer without negative exponents. √600 − √96?

Answer 1

√600 − √96

split into primes

600: √(2 * 2 * 2 * 3 * 5 * 5)

96: √(2 * 2 * 2 * 2 * 2 * 3)

find pairs of primes and separate pairs and non-pairs

600: √((2 * 2) * 2 * 3 * (5 * 5)) = √(2 * 2 * 5 * 5)sqrt(2 * 3) = 10√(6)

96: √((2 * 2) * (2 * 2) * 2 * 3) = √(2 * 2 * 2 * 2)sqrt(2 * 3) = 4√(6)

subtract

10√(6) - 4√(6) = 6√(6)

Answer 2

sqrt(600) = sqrt(100)sqrt(6) = 10*sqrt(6) 

sqrt(96) = sqrt( 24)*sqrt(4)  = sqrt(4)*sqrt(4)*sqrt(6) =  4*sqrt(6)  

so you have 

10*sqrt(6) - 4*sqrt(6)  = 6*sqrt(6) or  6√(6)