2020 · Q20
If x = √2, y = ∛3 and z = ⁶√6 then which one of the following is correct?
Elementary MathematicsNumber System
- Ay < x < z
- Bz < x < y
- Cz < y < x
- Dx < y < z
Explanation
Raise all three to the 6th power: x⁶ = (√2)⁶ = 8, y⁶ = (³√3)⁶ = 9, z⁶ = (⁶√6)⁶ = 6. Since 6 < 8 < 9, the order is z < x < y. Taking sixth roots preserves the strict inequalities, so z < x < y.