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Resources tagged with Square numbers similar to The Root Cause:

Other tags that relate to The Root Cause

Generalising. Theorem and contrapositive. Square numbers. Powers & roots. Mathematical reasoning & proof. Inequality/inequalities. Rational and irrational numbers. Patterned numbers. Manipulating algebraic expressions/formulae. Number theory.

There are 6 results

Broad Topics > Numbers and the Number System > Square numbers

The Root Cause

Stage: 5 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.)

Iff

Stage: 4 Challenge Level:

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.

Robert's Spreadsheet

Stage: 4 Challenge Level:

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

Generating Triples

Stage: 4 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?

Filling the Gaps

Stage: 4 Challenge Level:

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

Summing Squares

Stage: 4 Challenge Level:

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