Question

the value of {(2²)⅓}¼ is​

Answer 1

Answer:

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Answer 2

$( ({2}^{2} ) {}^{ \frac{1}{3} } ) {}^{ \frac{1}{4} } = {2}^{ \frac{1}{3 \times 2} } = {2}^{ \frac{1}{6} } = \sqrt[6]{2}$

For Approximating 2^(1/6)

$\lfloor \sqrt[6]{2} \rfloor = 1$

• First estimate is 1
• Second estimate ≤ 1/6. So, the 2nd Estimate is 1
• Third estimate can be calculated as

$e_{3} \le \frac{ 10({10}^{6} - 771561)}{6\times {11}^{5} } \approx2.36$

Therefore,

$\sqrt[6]{2} \approx1.12$