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Year 10
Higher

Identifying square factors to support simplifying surds

You can identify the highest square factor of any term including those written with algebra.

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New
New
Year 10
Higher

Identifying square factors to support simplifying surds

You can identify the highest square factor of any term including those written with algebra.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Numbers can be classified as surds or not surds.
  2. Square factors of numerical and algebraic terms can be identified.
  3. The highest square term is the one needed when simplifying surds.

Common misconception

Pupils may not fully simplify due to not identifying the highest square factor.

Encourage pupils to check the resulting radicand for any further square factors.

Keywords

  • Factor - A factor is a term which exactly divides another term.

  • Perfect square - A perfect square is a number that is the second exponent of an integer. It is usually shortened to square number.

  • 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.

If pupils do not identify the highest square factor then they will need to simplify again. Allow them to compare the approaches of using any square factor versus using the highest square factor to evaluate the efficiency.
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.
True or false? The group of integers would include values like 0.27
True
Correct answer: False
Q2.
An number is one that cannot be written in the form $$a \over b$$ where $$a$$ and $$b$$ are both integers and $$b \ne 0$$.
Correct Answer: irrational
Q3.
Identify the irrational number.
$$\sqrt 0$$
$$\sqrt 1$$
Correct answer: $$\sqrt 7$$
$$\sqrt 9$$
Q4.
Which of these is not a surd?
$$\sqrt {24}$$
$$\sqrt {35}$$
$$\sqrt {42}$$
Correct answer: $$\sqrt {49}$$
Q5.
Which of these is not a surd?
Correct answer: $$\sqrt[3] {27}$$
$$\sqrt[3] {33}$$
$$\sqrt[3] {39}$$
$$\sqrt[3] {42}$$
Q6.
Which of these is not a surd?
$$\sqrt {1 \over 6}$$
Correct answer: $$\sqrt {1 \over 81}$$
$$\sqrt {0.3}$$
$$\sqrt {0.95}$$

Exit quiz

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6 Questions

Q1.
Identify the surds.
Correct answer: $$\sqrt {ab}$$
$$\sqrt {a^2}$$
$$\sqrt {16 \times 3^2}$$
Correct answer: $$\sqrt 6$$
Q2.
Write an equivalent expression for $$\sqrt {2^4 \times 5^2}$$ that does not involve the radical sign.
Correct Answer: 20, twenty
Q3.
True or false? $$\sqrt {40}$$ is in its simplest form.
True
Correct answer: False
Q4.
Which of these is not a square factor of 64?
1
4
16
Correct answer: 32
Q5.
Which of these is not a square factor of 2700?
9
25
Correct answer: 64
900
Q6.
True or false? The highest square factor of 108 is 9.
True
Correct answer: False