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

Problem solving 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

Solving equations 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? Surds are a way of giving an answer exactly.

Arrange the surds from smallest to largest.

The perimeter of a rectangle is $$12 + 8\sqrt {2}$$. One of the lengths is $$6 + \sqrt {2}$$. Find the area.

The length of the line between (3,8) and (7,13) can be written in the form $$\sqrt {a}$$. What is the value of $$a$$?

Which of these shapes has a greater area?

Which of these shapes has a greater perimeter?

Order the fractions from smallest to largest.

What is the value of $$a + b - c$$ when $$a$$ = 7, $$b$$ = 21 and $$c$$ = 2.4

In order to rationalise $$(2 - \sqrt {3})$$ you would multiply by:

True or false? Pythagoras' theorem can only be used to find the length of the hypotenuse.

when the radicand is an integer and has no perfect square factors greater than 1

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

Problem solving with surds

Lesson outcome