Search by Topic

Resources tagged with Surds similar to Be Reasonable:

Filter by: Content type:
Age range:
Challenge level:

There are 19 results

Broad Topics > Numbers and the Number System > Surds

problem icon

Impossible Square?

Age 16 to 18 Challenge Level:

Can you make a square from these triangles?

problem icon

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?

problem icon

The Root of the Problem

Age 14 to 18 Challenge Level:

Find the sum of this series of surds.

problem icon

Pythagorean Fibs

Age 16 to 18 Challenge Level:

What have Fibonacci numbers got to do with Pythagorean triples?

problem icon

Golden Mathematics

Age 16 to 18

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

problem icon

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?

problem icon

Plus or Minus

Age 16 to 18 Challenge Level:

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

problem icon

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 ?

problem icon

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).

problem icon

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

problem icon

In Between

Age 16 to 18 Challenge Level:

Can you find the solution to this algebraic inequality?

problem icon

Bina-ring

Age 16 to 18 Challenge Level:

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

problem icon

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.

problem icon

Cube Roots

Age 16 to 18 Challenge Level:

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

problem icon

Fit for Photocopying

Age 14 to 16 Challenge Level:

Explore the relationships between different paper sizes.

problem icon

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.

problem icon

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?

problem icon

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.

problem icon

Pentabuild

Age 16 to 18 Challenge Level:

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