Or search by topic
There are 10 NRICH Mathematical resources connected to Square numbers, you may find related items under Properties of numbers.
Broad Topics > Properties of numbers > Square numbersSets 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?
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Can you find a rule which relates triangular numbers to square numbers?
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.