Multiplication of surds

Maths

Accuracy of final answers

Identifying square factors to support simplifying surds

Simplifying surds

Addition with 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

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

Calculate $$\sqrt {99} \times \sqrt {99}$$

Calculate $$\sqrt {3.9} \times \sqrt {3.9}$$

When multiplying surds, we {{}} the radicands.

Match up the multiplications with the simplied answers.

When dividing surds we {{}} the radicands.

Simplify the following expression: $$\sqrt {12} \div \sqrt {3}$$

Three of the surds are like surds. Which one is not?

$$10\sqrt {3} + a\sqrt {3} = -3\sqrt {3}$$. What is the value of $$a$$?

Simplify the expression $$\sqrt {12} + \sqrt {3} - \sqrt {27}$$

True or false? $$\sqrt {20}$$ and $$\sqrt {45}$$ are like terms.

Simplify the expression $$2\sqrt {15} + 3\sqrt {20} - 7\sqrt {80}$$

Multiplication of surds

Lesson outcome