Question

Express large and small. A=3root3,B=4root4,C=6root6 ?

Answer 1

`A < B < C`

Explanation:

Let,

`A=3sqrt3,B=4sqrt4, C=6sqrt6`

Squaring we get,

`A^2=(3sqrt3)^2=9xx3=27`

`B^2=(4sqrt4)^2=16xx4=64`

`C^2=(6sqrt6)^2=36xx6=216`

`i.e.A^2 < B^2 < C^2=>A < B < C`

OR

If your question is of type given below ,then see the following
answer.

`A=root(3)3, B=root(4)4 and C=root(6)6`

Now, `"LCM of : 3 , 4 , 6 is 12"`

So,

`A^12=(root(3)3)^12=(3^(1/3))^12=3^4=81`

`B^12=(root(4)4)^12=(4^(1/4))^12=4^3=64`

`C^12=(root(6)6)^12=(6^(1/6))^12=6^2=36`

`i.e. 36 < 64 < 81`

`=>C^12 < B^12 < A^12`

`=> C < B < A`