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Mathematics

3234\sqrt[4]{\sqrt[3]{3^2}} can be expressed as :

  1. 363^6

  2. 61/36^{1/3}

  3. 31/123^{1/12}

  4. 31/63^{1/6}

Rational Irrational Nos

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Answer

We know that,

xn=x1n\Rightarrow \sqrt[n]{x} = x^\dfrac{1}{n}

Solving,

32343234323×43212=316\Rightarrow \sqrt[4]{\sqrt[3]{3^2}} \\[1em] \Rightarrow \sqrt[4]{3^\dfrac{2}{3}} \\[1em] \Rightarrow 3^\dfrac{2}{3 \times 4} \\[1em] \Rightarrow 3^\dfrac{2}{12} \\[1em] = {3^\dfrac{1}{6}}

Hence, Option 4 is the correct option.

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