Other tags that relate to Proof Sorter - the Square Root of 2 Is Irrational
Mathematical reasoning & proof. Interactivities. Complex numbers. Continued fractions. Coordinates. Powers & roots. Dynamic geometry. Quadratic equations. Rational and irrational numbers. Proof by contradiction.There are 19 results
Broad Topics > Numbers and the Number System > Surds
Irrational Arithmagons
Age 16 to 18 Challenge Level:
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
Ab Surd Ity
Age 16 to 18 Challenge Level:
Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
Golden Mathematics
Age 16 to 18
A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.
Cube Roots
Age 16 to 18 Challenge Level:
Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.
Fit for Photocopying
Age 14 to 16 Challenge Level:
Explore the relationships between different paper sizes.
Plus or Minus
Age 16 to 18 Challenge Level:
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
Pythagorean Fibs
Age 16 to 18 Challenge Level:
What have Fibonacci numbers got to do with Pythagorean triples?
Fibonacci Fashion
Age 16 to 18 Challenge Level:
What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?
Golden Eggs
Age 16 to 18 Challenge Level:
Find a connection between the shape of a special ellipse and an infinite string of nested square roots.
Surds
Age 14 to 16 Challenge Level:
Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
Absurdity Again
Age 16 to 18 Challenge Level:
What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
Golden Construction
Age 16 to 18 Challenge Level:
Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
Strange Rectangle 2
Age 16 to 18 Challenge Level:
Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.
Baby Circle
Age 16 to 18 Challenge Level:
A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
Pentabuild
Age 16 to 18 Challenge Level:
Explain how to construct a regular pentagon accurately using a straight edge and compass.
NRICH is part of the family of activities in the Millennium Mathematics Project.