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

Rationalising a two 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 single 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

$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$

$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$

$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$

$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$

Match the brackets and their expanded form.

You can use the {{}} to make an integer from a surd expression.

What would you multiply $$(13 + \sqrt {17})$$ by to make an integer?

Express $${6} \over {2\sqrt {3} - 4}$$ in the form $$a(d+\sqrt {3})$$. What is the value of $$a$$?

Express $${6} \over {2\sqrt {3} - 4}$$ in the form $$a(d+\sqrt {3})$$. What is the value of $$d$$?

Expand the following expression: $$(3\sqrt {2} + \sqrt {3})(3\sqrt {2} - \sqrt {3})$$

Expand the following expression: $$(\sqrt {6} + 1)(\sqrt {6} - 1)$$

Expand the following expression: $$(2\sqrt {5} - 3\sqrt {3})(2\sqrt {5} + 3\sqrt {3})$$

Expand the following expression: $$(5\sqrt {7} - 4\sqrt {2})(5\sqrt {7} + 4\sqrt {2})$$

Expand the following expression: $$(\sqrt {8} + \sqrt {2})(\sqrt {2} - \sqrt {8})$$

Expand the following expression: $$(\sqrt {10} + 2\sqrt {5})(2\sqrt {5} - \sqrt {10})$$

Starter Quiz

Expand the following expression: $$(3\sqrt {2} + \sqrt {3})(3\sqrt {2} - \sqrt {3})$$