`sqrt(2root(3)(4sqrt(2root(3)(4.....).................)))` का मान क्‍या है?

Options

A. 2
B. `2^(2)`
C. `2^(3)`
D. `2^(5)`

Answer

A

Explanation

`x=sqrt(2root(3)(4sqrt(2root(3)(4))))………..`
`implies` Squaring both sides
`impliesx^(2)=2root(3)(4sqrt(2root(3)(4)))…….`
Now cubing both sides
`x^(6)=8xx4x`
`impliesx^(5)=32`
`impliesx^(5)=2^(5)`
`impliesx^(5)=2^(5)`
`impliesx=2`