( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }

Question

( \sqrt{11 }  +  \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 }   -  \sqrt{3} )^{ \frac{1}{3} }

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Sarah 2 weeks 2021-09-10T10:00:34+00:00 1 Answer 0 views 0

Answers ( )

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    2021-09-10T10:02:09+00:00

    ANSWER:

    ( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }   = 2

    GIVEN:

    ( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }

    TO FIND:

    The value of ( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }

    EXPLANATION:

    ( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }

    =  \sqrt[3]{ (\sqrt{11} +  \sqrt{3})( \sqrt{11}   -  \sqrt{3} )  }

    (A + B)(A – B) = (A² – B²)

    =  \sqrt[3]{ (\sqrt{11})^{2}   -  (\sqrt{3})^{2}  }

    =  \sqrt[3]{ 11 -  3  }

    =  \sqrt[3]{ 8 }

     = 2

    ( \sqrt{11 } + \sqrt{3} )^{ \frac{1}{3} } (\sqrt{11 } - \sqrt{3} )^{ \frac{1}{3} }   = 2

    SOME OTHER FORMULAE:

    • (A + B)² = A² + 2AB + B²
    • (A – B)² = A² – 2AB + B²
    • A² + B² = (A + B)² – 2AB
    • A² + B² = (A – B)² + 2AB
    • A³ – B³ = (A – B)(A² + AB + B²)
    • A³ + B³ = (A + B)(A² – AB + B²)
    • A³ + B³ + C³ = 3ABC ( A + B + C = 0)
    • (A – B)³ = A³ – B³ – 3AB(A – B)
    • (A + B)³ = A³ + B³ + 3AB(A + B)

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