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Anonymous
Anonymous asked in Education & ReferenceHomework Help · 2 months ago

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

### 2 Answers

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• √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)

• 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)

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