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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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  • 2 months ago

    √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)

  • Alan
    Lv 7
    2 months ago

    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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