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#