Question

Which of the following is an irrational number such that its 6th power is a rational number.

• A. $\sqrt[6]{62}$
• B. $\sqrt[8]{82}$
• C. 3
• D. 2

Answer 1

The correct option is A $\sqrt[6]{62}$

Let the irrational number be $6\sqrt{2}$ i.e., $2^{1/6}$
Then, the 6th power will be as follows:
$(2^{\frac{1}{6}}{)}^6=2^{\frac{1}{6}\times 6}=2$
Hence, 2 is a rational number.

So, option a is correct.