New
New
Year 10
Higher

Multiplication of surds

You can appreciate the structure that underpins multiplication of surds.

New
New
Year 10
Higher

Multiplication of surds

You can appreciate the structure that underpins multiplication of surds.

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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.

Common misconception

Pupils may not simplify after multiplying surds.

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

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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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

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