Question

Write the following in ascending order:

`7root(3)(5), 6root(3)(4) and 5root(3)(6)`

Answer 1

Since `7root(3)(5) = root(3)(7^3 xx 5) = root(3)(343 xx 5) = root(3)(1715)`
`6root(3)(4) = root(3)(6^3 xx 4) = root(3)(216 xx 4) = root(3)(864)`
`5root(3)(6) = root(3)(5^3 xx 4) = root(3)(125 xx 6) = root(3)(750)`
Since, 750 < 864 < 1715, we have `root(3)(750) < root(3)(864) < root(3)(1715)`.
Hence, `5root(3)(6) < 6root(3)(4) < 7root(3)(5)`.