Question

Suppose that w = 2^1/2, x = 3^1/3, y = 6^1/6 and z = 8^1/8. From among these number list, the biggest, second biggest numbers are-

Answer 1

Given :  w = 2^1/2, x = 3^1/3, y = 6^1/6 and z = 8^1/8

To find :  list, the biggest, second biggest numbers

Solution:

w = 2^1/2

=> w² = 2

x = 3^1/3

=> x³ = 3

y = 6^1/6

=> y⁶ = 6

z = 8^1/8

=> z⁸ = 8

w² = 2 => (w²)³ = 2³  => w⁶  =8

x³ = 3 => (x³)² = 3² => x⁶ = 9

y⁶ = 6

9 > 8 > 6

=> x⁶ >  w⁶ > y⁶

=> x > w > y

w² = 2 => (w²)⁴ = 2⁴ => w⁸ = 16

z⁸ = 8

=> w⁸> z⁸

=> w > z

x > w > y    and w > z

Hence biggest number is  x  and    second biggest number is  w

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