Question

Which one of the following is not equal to \[\left( \sqrt[3]{8} \right)^{- 1/2} ?\]

विकल्प

• \[\sqrt[3]{2}^{- 1/2}\]

• \[8^{- 1/6}\]

• \[\frac{1}{(\sqrt[3]{8} )^{1/2}}\]

• \[\frac{1}{\sqrt{2}}\]

Answer 1

 

We have to find the value of  `(3sqrt8)^(-1/2)`

So, 

 `(3sqrt8)^(-1/2) = (3sqrt(2xx 2xx 2))^(-1/2)`

`=(3sqrt(2^3))^(1/2)`

`2^(3 xx 1/3 xx -1/2)`

`2^(3 xx 1/3 xx -1/2)`

`(3sqrt8)^(-1/2) = 2^(-1/2)`

`= 1/(2^(1/2))`

`= 1/sqrt2`

Also,  `(sqrt8)^(-1/2) = 2 ^(-1/6)`