If \alpha_{1}=\sqrt^3{4},\alpha_{2}=\sqrt^4{5},\alpha_{3}=\sqrt^4{7} and \alpha_4=\sqrt3 then their collect order

Correct Answer is : α4>α3>α1>α2

\alpha_{1}>\alpha_{2}>\alpha_{3}>\alpha_{4}

\alpha_{2}>\alpha_{3}>\alpha_{4}>\alpha_{1}

\alpha_{3}>\alpha_{4}>\alpha_{1}>\alpha_{2}

\alpha_{4}>\alpha_{3}>\alpha_{1}>\alpha_{2}

AP ICET 2017 Shift 2 Paper

Question : 88 of 200

Marks: +1, -0

α_{1}=√^3{4},α_{2}=√^4{5},α_{3}=√^4{7}

and

α_4=√3

then their collect order

Solution:

LCM (2, 3, 4) = 12

a_{1}=(4)^{1/3}=(4^{4})^{1/12}=(256)^{1/12}

a_{2}=(5)^{1/4}=(5^{3})^{1/12}=(125)^{1/12}

a_{3}=(7)^{1/4}=(7^{3})^{1/12}=(343)^{1/12}

a_{4}=(3)^{1/2}\quad(3^{6})^{1/12}=(729)^{1/12}

∴

α_{4}>α_{3}>α_{1}>α_{2}

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