NRICH: Perfectly Square

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NRICH: Perfectly Square

The sums of the squares of three related numbers is also a perfect square – can you explain why?

We are first given that:

x1=2²+3²+6²
x2=3²+4²+12²
x3=4²+5²+20²

Then show that xₙ is always a perfect square.

Age 14 to 16

 

NRICH (University of Cambridge)
Math Topics
Algebra & Pre-Algebra, Quadratic Equations
High School, Educator
9th Grade, 10th Grade, 11th Grade
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NRICH: Perfectly Square

The sums of the squares of three related numbers is also a perfect square – can you explain why?

We are first given that:

x1=2²+3²+6²
x2=3²+4²+12²
x3=4²+5²+20²

Then show that xₙ is always a perfect square.

Age 14 to 16

 

NRICH (University of Cambridge)
Math Topics
Algebra & Pre-Algebra, Quadratic Equations
High School, Educator
9th Grade, 10th Grade, 11th Grade

What are you looking for?

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NRICH (University of Cambridge)

Website URL

Type of Resource

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