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Year 10
Higher

Applying the underlying structure of multiplication and division of surds

You can multiply and divide with surds.

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New
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Year 10
Higher

Applying the underlying structure of multiplication and division of surds

You can multiply and divide with surds.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The multiplication of surds can be generalised.
  2. √a × √b=√ab and √a × √(1/b) = √(a/b) = √a ÷ √b
  3. You may be able to simplify this product.

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 insist that a square root can be both positive and negative.

By convention, square root refers to the principal (positive) square root.

For √x to be a function, it can only have one output for each input. Graphing this using Desmos is a great way to demonstrate this and more on this will be covered in the functions and proof unit.
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).

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Starter quiz

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6 Questions

Q1.
Calculate $$\sqrt {0.764} \times \sqrt {0.764}$$
Correct Answer: 0.764
Q2.
Calculate $${9 \over \sqrt {3}} \times {9 \over \sqrt {3}}$$
Correct Answer: 27
Q3.
$$2\sqrt {5} \times \sqrt {2} = 2\sqrt {b}$$. What is the value of $$b$$?
Correct Answer: 10, ten
Q4.
$$\sqrt {6} \times \sqrt {4} \times 3\sqrt {10}\times \sqrt {10} = a\sqrt {6}$$. What is the value of $$a$$?
Correct Answer: 60, sixty
Q5.
Simplify the following expression: $$\sqrt {24} \div \sqrt {6}$$
Correct Answer: 2, two
Q6.
Evaluate the following expression: $$3\sqrt {20} \div \sqrt {5}$$
Correct Answer: 6, six

Exit quiz

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6 Questions

Q1.
Simplify the expression $$\sqrt {4ab} \times \sqrt {7a^{2}b}$$
$$2\sqrt {ab} \times \sqrt {7a^{2}b}$$
$$2\sqrt {ab} \times a\sqrt {7ab}$$
$$\sqrt {28a^{3}b^{2}}$$
Correct answer: $$2ab\sqrt {7a}$$
Q2.
Simplify the expression $$\sqrt {3 \over 4} \times \sqrt {1 \over 3}$$
Correct answer: $$1 \over 2$$
$$\sqrt {3 \over 12}$$
$$1 \over 4$$
$$\sqrt {1 \over 4}$$
Q3.
Simplify the expression: $$\sqrt {12} \times \sqrt {27}$$
$$\sqrt {324}$$
Correct answer: 18
$$2\sqrt {3} \times 3\sqrt {3}$$
54
Q4.
Simplify $$\sqrt {48} \times \sqrt {12}$$
Correct Answer: 24, twenty-four, twenty four
Q5.
Calculate $$(2\sqrt {48} - 5\sqrt {48}) \times \sqrt {12}$$
Correct Answer: -72
Q6.
Complete the rule for dividing surds: $$\sqrt {x \over y} = $$
$$\sqrt {x} \over y$$
$$x \over \sqrt {y}$$
Correct answer: $$\sqrt {x} \over \sqrt {y}$$