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

Rationalising a two term denominator

Maths

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.

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: $$(\sqrt {10} + 2\sqrt {5})(2\sqrt {5} - \sqrt {10})$$

This lesson will be removed by end of Summer Term 2025.

Rationalising a two term denominator

Lesson outcome

This lesson will be removed by end of Summer Term 2025.