# Resources tagged with: Surds

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Broad Topics > Numbers and the Number System > Surds ### Golden Mathematics

##### Age 16 to 18

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

##### Age 16 to 18 Challenge Level:

What have Fibonacci numbers got to do with Pythagorean triples? ### The Root of the Problem

##### Age 14 to 18 Challenge Level:

Find the sum of this series of surds. ### 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. ### Plus or Minus

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Explore the relationships between different paper sizes. ### Impossible Square?

##### Age 16 to 18 Challenge Level:

Can you make a square from these triangles? ### Bina-ring

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Can you find the solution to this algebraic inequality? ### 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 ### 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). ### 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? ### 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. ### 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. ### Cube Roots

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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