Arrange surds in descending order: 532,743,3 - Mathematics

Arrange surds in descending order:

`root(2)root(3)(5), root(3)root(4)(7), sqrt(sqrt(3)`

Sum

`root(2)root(3)(5) = root(6)(5), root(3)(root(4)(7)) = root(12)(7), sqrt(sqrt(3)) = root(4)(3)`

L.C.M of 6, 12 and 4 is 12

`root(2)root(3)(5) = root(6)(5) = root(12)(5^2) = root(12)(25)`

`root(3)(root(4)(7)) = root(12)(7) = root(12)(7)`

`sqrt(sqrt(3)) = root(4)(3) = root(12)(3^3) = root(12)(27)`

`root(12)(27) > root(12)(25) > root(12)(7)`

`sqrt(sqrt(3)) > root(2)root(3)(5) > root(3)(root(4)(7)`

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Order of a Surd

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Chapter 2: Real Numbers - Exercise 2.6 [Page 68]

Chapter 2 Real Numbers
Exercise 2.6 | Q 4. (ii) | Page 68

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