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Lesson 5 of 12
  • Year 10
  • Higher

Multiplication of surds

I can appreciate the structure that underpins multiplication of surds.

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View unit
Lesson 5 of 12
New
New
  • Year 10
  • Higher

Multiplication of surds

I can appreciate the structure that underpins multiplication of surds.

Download all

Lesson details

Key learning points

  1. The square root operation is equivalent to the exponent 0.5 where the base is the term under the square root.
  2. You can deduce this as squaring and square rooting are inverse operations.
  3. Since the exponents for each term are the same, they can be combined.

Keywords

  • Surd - A surd is an irrational number expressed as the root of a rational number.

  • Radical - The root sign is the radical symbol.

  • Radicand - The radicand is the value inside the radical symbol.

Common misconception

Pupils may not simplify after multiplying surds.

Surds should always be written in their simplest form for the final answer.


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

This lesson builds on the learning from arithmetic procedures: index laws (unit 4) which pupils should be familiar with before starting this lesson. It is suggested that this link is highlighted during the lesson to aid pupils in seeing connections.
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Licence

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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Prior knowledge starter quiz

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6 Questions

Q1.
Three of the surds are like surds. Which one is not?

$$\sqrt {48}$$
$$2\sqrt {27}$$
$$2\sqrt {12}$$
Correct answer: $$2\sqrt {18}$$

Q2.
Three of the surds are like surds. Which one is not?

$$-5\sqrt {80}$$
Correct answer: $$-5\sqrt {30}$$
$$a\sqrt {20}$$
$$b\sqrt {45}$$

Q3.
$$10\sqrt {3} + a\sqrt {3} = -3\sqrt {3}$$. What is the value of $$a$$?

Correct Answer: -13

Q4.
Simplify the expression $$\sqrt {12} + \sqrt {3} - \sqrt {27}$$

$$3\sqrt {3} - \sqrt {27}$$
$$-4\sqrt {3}$$
$$6\sqrt {3}$$
Correct answer: 0

Q5.
True or false? $$\sqrt {20}$$ and $$\sqrt {45}$$ are like terms.

True
Correct answer: False

Q6.
Simplify the expression $$2\sqrt {15} + 3\sqrt {20} - 7\sqrt {80}$$

$$2\sqrt {15} - 100\sqrt {5}$$
Correct answer: $$2\sqrt {15} - 22\sqrt {5}$$
$$2\sqrt {15} - 4\sqrt {5}$$
$$2\sqrt {15} - 2\sqrt {5}$$

Assessment exit quiz

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6 Questions

Q1.
Calculate $$\sqrt {99} \times \sqrt {99}$$

Correct Answer: 99

Q2.
Calculate $$\sqrt {3.9} \times \sqrt {3.9}$$

Correct Answer: 3.9

Q3.
When multiplying surds, we the radicands.

Correct Answer: multiply, times

Q4.
Match up the multiplications with the simplied answers.

Correct Answer:$$2\sqrt {6}$$,$$\sqrt {6} \times \sqrt {4}$$

$$\sqrt {6} \times \sqrt {4}$$

Correct Answer:30,$$3\sqrt {10}\times \sqrt {10}$$

$$3\sqrt {10}\times \sqrt {10}$$

Correct Answer:$$7\sqrt {2}$$,$$\sqrt {14} \times \sqrt {7}$$

$$\sqrt {14} \times \sqrt {7}$$

Correct Answer:$$3\sqrt {2}$$,$$\sqrt {3} \times \sqrt {6}$$

$$\sqrt {3} \times \sqrt {6}$$

Q5.
When dividing surds we the radicands.

Correct Answer: divide

Q6.
Simplify the following expression: $$\sqrt {12} \div \sqrt {3}$$

Correct Answer: 2