Math 2.0

Number theory Theorem

Irrationality of the square root of a prime

Builds on Irrational numberSquare root

Statement

Let pp be a prime number. Then p\sqrt{p} is an irrational number.

Remarks

This generalizes the irrationality of the square root of 2. More generally, the square root of a natural number nn is irrational unless nn is a perfect square. See the roots of integers.

Reading path

To understand this page from the ground up, read these 9 pages in order. The foundations come first.

Show the path as a graph
Rational numbers, object, no evidence levelRational numbersobjectReal numbers, object, no evidence levelReal numbersobjectSet bounded above, definition, no evidence levelSet bounded abovedefinitionIrrational number, definition, no evidence levelIrrational numberdefinitionSupremum, definition, no evidence levelSupremumdefinitionCompleteness axiom, statement, no evidence levelCompleteness axiomstatementExistence of square roots of nonnegative reals, statement, no evidence levelExistence of square r…statementSquare root, definition, no evidence levelSquare rootdefinitionIrrationality of the square root of a prime, statement, no evidence levelIrrationality of the …statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Rational numbers object
  2. Real numbers object
  3. Set bounded above definition
  4. Irrational number definition
  5. Supremum definition
  6. Completeness axiom statement
  7. Existence of square roots of nonnegative reals statement
  8. Square root definition
  9. Irrationality of the square root of a prime statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Irrational_number, Square roots
About this page
Tag0YHFMXJJAZ
URIm2://0YHFMXJJAZ
Kindstatement, theorem
WritingW0 stub
MSC11J72
StatusThis copy of the site has no build data. Run m2 status 0YHFMXJJAZ.
UsesIrrational number, Square root

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