Question

Amongst the following which is greater:

\(\left(\dfrac{1}{2}\right)^{1/2}\; or \left(\dfrac{1}{3}\right)^{1/3}\)

1. \(\left(\dfrac{1}{2}\right)^{1/2}\)
2. \(\left(\dfrac{1}{3}\right)^{1/3}\)
3. Both are equal
4. None of the above

Answer 1

Correct Answer - Option 1 : \(\left(\dfrac{1}{2}\right)^{1/2}\)

Calculation:

As, given

\(\left(\dfrac{1}{2}\right)^{1/2}\; or \left(\dfrac{1}{3}\right)^{1/3}\)

As, 1/2 = 0.5

And, 1/3 = 0.333

Now, the power of 0.5 is greater than the power of 0.333, and also 0.5 > 0.333

 \(\left(\dfrac{1}{2}\right)^{1/2}\ is \ greater \ than \left(\dfrac{1}{3}\right)^{1/3}\)

∴ \(\left(\dfrac{1}{2}\right)^{1/2}\;\) is greater.