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.

Simplifying surds

Maths

Accuracy of final answers

Identifying square factors to support 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 surd is in its simplest form when the {{}} is an integer with no perfect square factors greater than 1.

Which of these surds are in their simplest form?

$$\sqrt {72}$$ simplifies to $$6\sqrt a$$. What is the value of $$a$$?

$$4\sqrt {72}$$ simplifies to $$k\sqrt 2$$. What is the value of $$k$$?

$$7\sqrt {48}$$ simplifies to $$h\sqrt 3$$. What is the value of $$h$$?

$$2\sqrt {180}$$ simplifies to $$d\sqrt 5$$. What is the value of $$d$$?

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

True or false? $$\sqrt {41}$$ 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 225 is 25.

Starter Quiz

Identify the surds.