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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
New
Year 10
Higher

Applying the underlying structure of multiplication and division of surds

You can multiply and divide with surds.

Download all resources
Share activities with pupils

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.

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.

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.

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: $$\sqrt {x} \over \sqrt {y}$$