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Resources tagged with Surds similar to Weekly Challenge 16: Archimedes Numerical Roots:

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Broad Topics > Numbers and the Number System > Surds

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Ab Surd Ity

Stage: 5 Challenge Level: Challenge Level:1

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

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The Root of the Problem

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the sum of the series.

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Golden Mathematics

Stage: 5

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

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Fibonacci Fashion

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

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Plus or Minus

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

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Fit for Photocopying

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Photocopiers can reduce from A3 to A4 without distorting the image. Explore the relationships between different paper sizes that make this possible.

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Pythagorean Fibs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What have Fibonacci numbers got to do with Pythagorean triples?

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Bina-ring

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate powers of numbers of the form (1 + sqrt 2).

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Surds

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

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

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Absurdity Again

Stage: 5 Challenge Level: Challenge Level:1

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

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Baby Circle

Stage: 5 Challenge Level: Challenge Level:1

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?

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Irrational Arithmagons

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

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In Between

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the solution to this algebraic inequality?

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Cube Roots

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.

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Impossible Square?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make a square from these triangles?

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Strange Rectangle 2

Stage: 5 Challenge Level: Challenge Level:1

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

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Pentabuild

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explain how to construct a regular pentagon accurately using a straight edge and compass.

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Golden Eggs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

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Origami Shapes

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Take a sheet of A4 paper and place it in landscape format. Fold up the bottom left corner to the top so the double thickness is a 45,45,90 triangle. Fold up the bottom right corner to meet the. . . .

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Golden Construction

Stage: 5 Challenge Level: Challenge Level:1

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.


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