Rational and irrational numbers

There are 24 NRICH Mathematical resources connected to Rational and irrational numbers
Making Rectangles, Making Squares
problem

Making Rectangles, Making Squares

Age
11 to 14
Challenge level
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How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Rationals Between...
problem

Rationals Between...

Age
14 to 16
Challenge level
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What fractions can you find between the square roots of 65 and 67?
Rational Roots
problem

Rational Roots

Age
16 to 18
Challenge level
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Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
Good Approximations
problem

Good Approximations

Age
16 to 18
Challenge level
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Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Be reasonable
problem

Be reasonable

Age
16 to 18
Challenge level
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Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
What Are Numbers?
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What Are Numbers?

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.
The Dangerous Ratio
article

The Dangerous Ratio

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.
All is Number
article

All is Number

Read all about Pythagoras' mathematical discoveries in this article written for students.