simply the following  \sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{4} \div \sqrt{5} }

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simply the following

 \sqrt{4 +  \sqrt{4} +  \sqrt{4}   +  \sqrt{4}  \div  \sqrt{5} }

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Allison 1 month 2021-10-28T00:00:24+00:00 2 Answers 0 views 0

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    0
    2021-10-28T00:01:25+00:00

    your answer..

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    0
    2021-10-28T00:01:37+00:00

    \sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{4} \div \sqrt{5} }

    write the division as fraction

    \sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{ \frac{4}{ \sqrt{5} } }  }

    Rationalize the denominator

    \sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{ \frac{4 \sqrt{5} }{5} }  }

    to take a root of fraction take the the root of the number and denominator separately

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{ \sqrt{4 \sqrt{5} } }{ \sqrt{5} }  }

    Simplify the redical expression

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{2 \sqrt{ \sqrt{5} } }{5}  }

     \bold{using \sqrt{m \sqrt{n \sqrt{a} } } } =   \sqrt[mn]{a}  Simply the expression

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{ 2\sqrt[4]{5} }{ \sqrt{5} }  }

    rationalize the denominator

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{2 \sqrt[4]{5} \sqrt{5}  }{5}  }

     \bold{using \:  \sqrt[n]{a}  =   \sqrt[mn]{ {a}^{m} } }expand the expression

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{2 \sqrt[4]{5}{   \sqrt[4]{ {5}^{2} }  }  }{5}  }

    the product of roots with the same index is equal to the root of the product

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{2 \sqrt[4]{5 \times  {5}^{2} } } {5}  }

    calculate the product

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{2 \sqrt[4]{ {5}^{3} }  }{5}  }

    evalute the power

    \sqrt{4 + \sqrt{4} + \sqrt{4} +  \frac{2 \sqrt[4]{125}  }{5}  }

    Alternate form

    ≈ 2.55187

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