Square numbers

There are 44 NRICH Mathematical resources connected to Square numbers
Square Triangle
problem

Square Triangle

Age
11 to 14
Challenge level
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How many triangles have all three angles perfect squares (in degrees)?
Square subtraction
problem
Favourite

Square subtraction

Age
7 to 11
Challenge level
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Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Few and far between?
problem

Few and far between?

Age
16 to 18
Challenge level
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Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Filling the gaps
problem
Favourite

Filling the gaps

Age
14 to 16
Challenge level
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Which numbers can we write as a sum of square numbers?
Generating Triples
problem
Favourite

Generating Triples

Age
14 to 16
Challenge level
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Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Pythagorean Quadruple
problem

Pythagorean Quadruple

Age
14 to 16
Challenge level
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The sum of three square numbers equals $121$. What can those numbers be...
No Square Sums
problem

No Square Sums

Age
14 to 16
Challenge level
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How many numbers do you need to remove to avoid making a perfect square?
Robert's spreadsheet
problem

Robert's spreadsheet

Age
14 to 16
Challenge level
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Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Light the Lights Again
problem
Favourite

Light the Lights Again

Age
7 to 11
Challenge level
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Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Four Coloured Lights
problem

Four Coloured Lights

Age
11 to 14
Challenge level
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Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?