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zackb

simplify by reducig the index of the radical

  • one year ago
  • one year ago

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  1. zackb
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    \[\sqrt[12]{125x ^{3}}\]

    • one year ago
  2. zzr0ck3r
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    = (125*x^3)^(1/12) - (5^3*x^3)^(1/12) = 5^(3/12)*x(^(3/12) = 5^(1/4)*x^(1/4) = (5x)^(1/4) = \[\sqrt[4]{5x}\]

    • one year ago
  3. zackb
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    thanks

    • one year ago
  4. Calcmathlete
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    Remember how you can rewrite it as a rational exponent. \[\sqrt[12]{125x^3} \implies \sqrt[12]{(5x)^3} \implies (5x)^{\frac{3}{12}} \implies (5x)^{\frac14} \implies \sqrt[4]{5x}\]See how it works? I just used this rule below: \[\sqrt[n]{y^x} \implies y^{\frac xn}\]

    • one year ago
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