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

Solving equations with surds

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

Rationalising a two term denominator

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

Solve $$x\sqrt {180} - 30 = x\sqrt {80}$$ and write your answer in the form $$a\sqrt {b}$$. State the value of $$b$$.

Solve $$x\sqrt {180} - 30 = x\sqrt {80}$$ and write your answer in the form $$a\sqrt {b}$$. State the value of $$a$$.

True or false? The solutions to $$2x^{2} + 9x - 2 = 0$$ are $$x = -9 \pm \sqrt {97}$$

True or false? The solutions to $$x^{2} + 5x - 4 = 0$$ are $$x = \frac{1}{2} (-5 \pm \sqrt {41})$$

Is this statement true or false? "There are always two solutions to a quadratic equation"

Solve the equation $$2(3x - 10) - 3(7 - 5x) = 484$$

$$x^{2} + 2bx + c = (x + b)^{2} - b^{2} + c$$ is known as completing the {{}} .

Select the correct form for the quadratic formula.

Simplify the expression: $$\sqrt {12} \times \sqrt {30}$$

Solving equations with surds

Lesson outcome