Addition with surds

Maths

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 $$d$$?

This lesson will be removed by end of Summer Term 2025.

Addition with surds

Lesson outcome

This lesson will be removed by end of Summer Term 2025.