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Rational or irrational roots, step by step

A root sign does not make a number irrational — √16 is 4.

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The question

Rational or irrational?

√50

√50
√50
it never comes out
√50isirrational
  1. One question decides it: can this be written as a fraction of two whole numbers? Not "does it look tidy", and not "is there a root sign" — those are the two guesses that go wrong.
  2. Try to work the root out and it does not come out: 50 is not a perfect square, so its root never ends and never repeats.
  3. So it cannot be written as a fraction of two whole numbers. That makes it irrational.

How it works.

  1. 01

    One question decides it: can this be written as a fraction of two whole numbers? Not "does it look tidy", and not "is there a root sign" — those are the two guesses that go wrong.

  2. 02

    Try to work the root out and it does not come out: 50 is not a perfect square, so its root never ends and never repeats.

  3. 03

    So it cannot be written as a fraction of two whole numbers. That makes it irrational.

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