Addition with surds

Maths

Accuracy of final answers

Identifying square factors to support simplifying surds

Simplifying 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

Three of the surds are like surds. Which one is not?

$$4\sqrt {6} - a\sqrt {6} = -5\sqrt {6}$$. What is the value of $$a$$?

After gathering like terms in the expression $$4 - 3\sqrt b + 7\sqrt {bc} + 3\sqrt b - 20 - \sqrt {bc}$$, how many terms will be in the resulting expression?

Is the statement "It is **always** best to simplify before adding surds"

Calculate the perimeter of a square with side length $$\sqrt {18} + \sqrt {20}$$. Give your answer as simply as possible.

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

Which of these surds are in their simplest form?

$$\sqrt {18}$$ simplifies to $$a\sqrt 2$$. What is the value of $$a$$?

$$3\sqrt {76}$$ simplifies to $$k\sqrt {19}$$. What is the value of $$k$$?

$$3\sqrt {125}$$ simplifies to $$h\sqrt 5$$. What is the value of $$h$$?

$$9\sqrt {98}$$ simplifies to $$d\sqrt 2$$. What is the value of $$d$$?

Starter Quiz

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