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Year 10
Higher

Rationalising a two term denominator

You can use the technique of rationalising the denominator to transform a fraction to an equivalent fraction.

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New
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Year 10
Higher

Rationalising a two term denominator

You can use the technique of rationalising the denominator to transform a fraction to an equivalent fraction.

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Lesson details

Key learning points

  1. Fractions should be given in their simplest term.
  2. The denominator should be written as simply as possible.
  3. Combining your knowledge of equivalent fractions and the distributive law will help.

Keywords

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

Common misconception

Pupils may struggle to see why using the difference of two squares is important.

The grid method for multiplication can be used to explore why two of the terms cancel each other.

This learning relates directly to the difference of two squares learning that took place in algebaic manipulation (unit 1) and that unit can be used to support the learning in this 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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Expand the following expression: $$(3\sqrt {2} + \sqrt {3})(3\sqrt {2} - \sqrt {3})$$
Correct Answer: 15
Q2.
Expand the following expression: $$(\sqrt {6} + 1)(\sqrt {6} - 1)$$
Correct Answer: 5
Q3.
Expand the following expression: $$(2\sqrt {5} - 3\sqrt {3})(2\sqrt {5} + 3\sqrt {3})$$
Correct Answer: -7
Q4.
Expand the following expression: $$(5\sqrt {7} - 4\sqrt {2})(5\sqrt {7} + 4\sqrt {2})$$
Correct Answer: 143
Q5.
Expand the following expression: $$(\sqrt {8} + \sqrt {2})(\sqrt {2} - \sqrt {8})$$
Correct Answer: -6
Q6.
Expand the following expression: $$(\sqrt {10} + 2\sqrt {5})(2\sqrt {5} - \sqrt {10})$$
Correct Answer: 10

Exit quiz

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6 Questions

Q1.
Match the brackets and their expanded form.
Correct Answer:12,$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$

$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$

Correct Answer:$$28+8\sqrt {10}$$,$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$

$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$

Correct Answer:-12,$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$

$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$

Correct Answer:$$-28+8\sqrt {10}$$,$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$

$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$

Q2.
You can use the to make an integer from a surd expression.
Correct Answer: difference of two squares
Q3.
What would you multiply $$(13 + \sqrt {17})$$ by to make an integer?
Correct answer: $$(13 - \sqrt {17})$$
$$(\sqrt {17} + 13)$$
Correct answer: $$(\sqrt {17} - 13)$$
$$(-\sqrt {17} - 13)$$
Q4.
Simplify $${{8} \over {4 - \sqrt {5}}}$$
$${{32 - 8\sqrt {5}} \over {16 + 5}}$$
$${{32 - 8\sqrt {5}} \over {21}}$$
$${{32 + 8\sqrt {5}} \over {16 - 5}}$$
Correct answer: $${{32 + 8\sqrt {5}} \over {11}}$$
Q5.
Express $${6} \over {2\sqrt {3} - 4}$$ in the form $$a(d+\sqrt {3})$$. What is the value of $$a$$?
-6
Correct answer: -3
2
3
Q6.
Express $${6} \over {2\sqrt {3} - 4}$$ in the form $$a(d+\sqrt {3})$$. What is the value of $$d$$?
-6
-3
Correct answer: 2
3