Search by Topic

Resources tagged with Square numbers similar to The Root Cause:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 6 results

Broad Topics > Numbers and the Number System > Square numbers

problem icon

The Root Cause

Stage: 5 Challenge Level: Challenge Level:1

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.)

problem icon

Iff

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.

problem icon

Robert's Spreadsheet

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Generating Triples

Stage: 4 Challenge Level: Challenge Level:1

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?

problem icon

Filling the Gaps

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Summing Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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