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

The distributive law 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

Match the statements with the equations that demonstrate each law.

Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$. What is the value of $$a$$?

Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$, where $$b>d$$. What is the value of $$b$$?

Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$. What is the value of $$c$$?

Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$, where $$b>d$$. What is the value of $$d$$?

Simplify the expression $$\sqrt {24a^{2}b} \times \sqrt {3a^{2}b}$$

Simplify the expression $$\sqrt {24 \over 30} \times \sqrt {5 \over 25}$$

$$\sqrt {28} \times \sqrt {80} = w\sqrt {b}$$. Write down the value of $$b$$.

$$\sqrt {28} \times \sqrt {80} = w\sqrt {b}$$. Write down the value of $$w$$.

$$4\sqrt {3} + 9\sqrt {3} - 16\sqrt {3}$$

Simplify the expression: $$\sqrt {12} + \sqrt {27} - \sqrt {48}$$

$$25\sqrt {3} - 9\sqrt {3} + 16\sqrt {3}$$

Simplify the expression: $$\sqrt {75} - \sqrt {27} + \sqrt {48}$$

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

The distributive law with surds

Lesson outcome

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