A perfect square is a number that is the second exponent of an integer. It is usually shortened to square number.

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

The radicand is the value inside the radical symbol.

Identifying square factors to support simplifying surds

Maths

Accuracy of final answers

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

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

Write an equivalent expression for $$\sqrt {2^4 \times 5^2}$$ that does not involve the radical sign.

True or false? $$\sqrt {40}$$ is in its simplest form.

Which of these is **not** a square factor of 64?

Which of these is **not** a square factor of 2700?

True or false? The highest square factor of 108 is 9.

True or false? The group of integers would include values like 0.27

An {{}} number is one that **cannot** be written in the form $$a \over b$$ where $$a$$ and $$b$$ are both integers and $$b \ne 0$$.

Identifying square factors to support simplifying surds

Lesson outcome