# Resources tagged with: Surds

### There are 19 results

Broad Topics >

Numbers and the Number System > Surds

##### Age 16 to 18

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

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

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

##### 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).

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

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

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

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

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

What have Fibonacci numbers got to do with Pythagorean triples?

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

Can you find the solution to this algebraic inequality?

##### 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.

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

Can you make a square from these triangles?

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

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

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

Find the sum of this series of surds.

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

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

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

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

##### 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?

##### 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.

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

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

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

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

##### 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

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

Explore the relationships between different paper sizes.