When A = $root(3)3$ , B = $root(4)4$ , C = $root(6)6$ , find the relationship. which number is the correct number? 1. A<B<C 2. A<C<B 3. B<A<C 4. B<C<A 5. C<B<A

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Answer 1 · 2018-04-20T10:16:29

$5 . C < B < A$

Here,

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

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

So,

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

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

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

$i.e. 36 < 64 < 81$

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

$=> C < B < A$

When A = root(3)3root(3)3, B = root(4)4root(4)4, C = root(6)6root(6)6 , find the relationship. which number is the correct number? 1. A<B<C 2. A<C<B 3. B<A<C 4. B<C<A 5. C<B<A