Adding and subtracting surds. Parts b) and c) involve simplification of surds.

The student is given a value of $\cos(\theta)$ and has to find $\theta$.

Shows how to use subexpressions to represent randomly-chosen fractions of $\pi$ and surds, and have them displayed nicely.

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Translated to German, minor changes to advice section.

Original: https://numbas.mathcentre.ac.uk/question/22497/surds-simplification/ by Lauren Richards.

Quadratwurzeln vereinfachen, Nenner rational machen

Deutsche Übersetzung von https://numbas.mathcentre.ac.uk/question/22587/using-surds-rationalising-the-denominator/ von Elliott Fletcher

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Translated to German, made some minor changes to Advice section.

Original: https://numbas.mathcentre.ac.uk/question/22555/rationalising-the-denominator-surds/ by Lauren Richards

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Some questions on working with surds.

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

Using Pythagoras' theorem to determine the hypotenuse, where side lengths include surds and students enter using sqrt syntax

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

 Some questions on working with surds.

Some questions on working with surds.

Some questions on working with surds.

Rationalising Denominator (complex)

Rationalising the Denominator (Simple)

No description given

In this question the student will be asked to manipulate surds and rationalise the denominator of a fraction when it is a surd.

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

Using Pythagoras' theorem to determine the hypotenuse, where side lengths include surds and students enter using sqrt syntax