### There are 10 results

Broad Topics >

Numbers and the Number System > Square numbers

##### Age 16 to 18 Challenge Level:

Prove that if a is a natural number and the square root of a is
rational, then it is a square number (an integer n^2 for some
integer n.)

##### Age 14 to 18 Challenge Level:

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

##### Age 14 to 16 Challenge Level:

Robert noticed some interesting patterns when he highlighted square
numbers in a spreadsheet. Can you prove that the patterns will
continue?

##### Age 14 to 16 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

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!

##### Age 14 to 16 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

##### Age 14 to 16 Challenge Level:

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

##### Age 14 to 16 Challenge Level:

Which numbers can we write as a sum of square numbers?

##### Age 14 to 18 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

##### Age 14 to 16 Challenge Level:

Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?