A recurring decimal is one that has a digit or sequence of digits that repeat endlessly.

A terminating decimal is one that has a finite number of digits after the decimal point.

A rational number is one that can be written in the form a/b where a and b are integers and b is not equal to 0.

An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0.

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

Accuracy of final answers

Maths

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

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

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

The radicand is the value inside the radical symbol.

Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

A surd is in its simplest form when the radicand is an integer with no perfect square factors greater than 1.

The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

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