A surd is an irrational number expressed as the root of a rational number.

Rationalising a single term denominator

Maths

Accuracy of final answers

Identifying square factors to support simplifying surds

Simplifying surds

Addition with surds

Multiplication of surds

Applying the underlying structure of multiplication and division of surds

The distributive law with surds

The distributive law with two or more binomials

Rationalising a two term denominator

Solving equations with surds

Problem solving with surds

In the prior unit, pupils explored the concept of square root, including calculating this on their calculators. In this unit, pupils work with surds and the notion that a surd is both an operation and the result of that operation.

In this unit pupils will learn how to recognise surds, handle them in calculations and rationalise fractions with surds as denominators.

Surds

True or false? $$\sqrt {7 {1\over9}}$$ is in its simplest form.

Simplify $$\sqrt {30 {1\over4}}$$. Write your answer in decimal notation. 

What should you multiply by to rationalise $$5 \over \sqrt {5}$$ ?

$${3 + 2\sqrt {3}} \over {3 + 2\sqrt {3}}$$

What should you multiply by to rationalise $${3 + 2\sqrt {3}} \over \sqrt {7}$$ ?

Rationalise the denominator $${3\sqrt {3}} \over {2\sqrt {2}}$$

Rationalise the denominator $${36} \over {3\sqrt {4}}$$

Which of these fractions are written in simplest form?

Evaluate $$\sqrt {41} \times \sqrt {41}$$

Evaluate $$\sqrt {0.3999} \times \sqrt {0.3999}$$

If the radicand is rational, then squaring the surd results in a {{}} number.

True or false? An equivalent fraction can be created by multiplying the denominator by the scale factor.

Rationalising a single term denominator

Lesson outcome