Question

raise irrational number to rational power and get a rational number

Answer 1

9514 1404 393

Answer:

  (√2)² = 2

Step-by-step explanation:

You can do this for any rational root of a rational number. Simple examples are squares and cubes:

  (√5)^2 = 5 . . . . . . √5 is irrational

  (∛6)^3 = 6 . . . . . . . ∛6 is irrational

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You can also do it with other rational roots:

  x = 83^(2/3) is irrational

  x^(3/2) = 83 is rational