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Year 10
Higher

The distributive law with surds

I can apply the distributive law to expressions involving surds.

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Year 10
Higher

The distributive law with surds

I can apply the distributive law to expressions involving surds.

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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Knowing how to perform arithmetic operations with surds means the distributive law can be considered.
  2. Surds could be seen in either the term or the binomial.

Keywords

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

Common misconception

Pupils may struggle with applying the distributive law to expressions involving surds.

The area model can be used here to demonstrate how terms are multiplied when expanding the bracket.


To help you plan your year 10 maths lesson on: The distributive law with surds, download all teaching resources for free and adapt to suit your pupils' needs...

The area model appears at the start of the first learning cycle to remind pupils about the distributive law and it can be used throughout the lesson to support pupils who are struggling with expanding brackets.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Simplify the expression $$\sqrt {24a^{2}b} \times \sqrt {3a^{2}b}$$
$$2a\sqrt {6b} \times a\sqrt {3b}$$
Correct answer: $$6a^{2}b\sqrt {2}$$
$$2a^{2}\sqrt {18b^{2}}$$
$$18a^{2}b\sqrt {2}$$
Q2.
Simplify the expression $$\sqrt {24 \over 30} \times \sqrt {5 \over 25}$$
Correct Answer: 0.4, 2/5, $$2 \over 5$$
Q3.
$$\sqrt {28} \times \sqrt {80} = w\sqrt {b}$$. Write down the value of $$b$$.
Correct Answer: 35
Q4.
$$\sqrt {28} \times \sqrt {80} = w\sqrt {b}$$. Write down the value of $$w$$.
Correct Answer: 8
Q5.
Simplify the expression: $$\sqrt {12} + \sqrt {27} - \sqrt {48}$$
$$-3\sqrt {3}$$
$$4\sqrt {3} + 9\sqrt {3} - 16\sqrt {3}$$
Correct answer: $$\sqrt {3}$$
$$2\sqrt {3} + 3\sqrt {3} - 4\sqrt {3}$$
Q6.
Simplify the expression: $$\sqrt {75} - \sqrt {27} + \sqrt {48}$$
Correct answer: $$6\sqrt {3}$$
$$5\sqrt {3} - 3\sqrt {3} + 4\sqrt {3}$$
$$32\sqrt {3}$$
$$25\sqrt {3} - 9\sqrt {3} + 16\sqrt {3}$$

Exit quiz

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6 Questions

Q1.
Match the statements with the equations that demonstrate each law.
Correct Answer:The distributive law,$$a(b+c) = ab + ac$$
tick

$$a(b+c) = ab + ac$$

Correct Answer:The associative law,$$(a+b) + c = a + (b + c)$$
tick

$$(a+b) + c = a + (b + c)$$

Correct Answer:The commutative law,$$a+b = b+a$$
tick

$$a+b = b+a$$

Q2.
Expand $$4(3\sqrt {5} + \sqrt {27})$$
$$12\sqrt {5} + 4\sqrt {3}$$
Correct answer: $$12\sqrt {5} + 12\sqrt {3}$$
$$12\sqrt {5} + 3\sqrt {3}$$
$$12\sqrt {5} + 4\sqrt {27}$$
Q3.
Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$. What is the value of $$a$$?
Correct answer: 2
4
6
15
Q4.
Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$, where $$b>d$$. What is the value of $$b$$?
2
4
6
Correct answer: 15
Q5.
Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$. What is the value of $$c$$?
Correct answer: 2
4
6
15
Q6.
Write $$\sqrt {3}(\sqrt {8} + \sqrt {20})$$ in the form $$a\sqrt {b} + c\sqrt {d}$$, where $$b>d$$. What is the value of $$d$$?
2
4
Correct answer: 6
15