which is largest root 3 4 or 5, Surds and Indices, General Mathematics

Question:Which is largest: `root(3)(4)` or `root(4)(5)`

Answer `:. \ root(3)(4)`

 = `4^(1/3)`

 = `4^((1/3 xx 3/3))`

 = `4^(4/12)`

 = `(4^4)^(1/12)`

 = `256^(1/12)`


`:. \ root(4)(5)`

 = `5^(1/4)`

 = `4^((1/4 xx 3/3))`

 = `5^(3/12)`

 = `(4^3)^(1/12)`

 = `125^(1/12)`

 Clearly. `(256)^(1/12)` > `(125)^(1/12)`

 or `root(3)(4)` > `root(4)(5)`

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Which is largest: `root(3)(4)` or `root(4)(5)`

Question:Which is largest: `root(3)(4)` or `root(4)(5)`

Answer `:. \ root(3)(4)` = `4^(1/3)` = `4^((1/3 xx 3/3))` = `4^(4/12)` = `(4^4)^(1/12)` = `256^(1/12)` `:. \ root(4)(5)` = `5^(1/4)` = `4^((1/4 xx 3/3))` = `5^(3/12)` = `(4^3)^(1/12)` = `125^(1/12)` Clearly. `(256)^(1/12)` > `(125)^(1/12)` or `root(3)(4)` > `root(4)(5)`