The radicand should be as small as possible.
If any of the radicand's factors are square numbers then the surd can be simplified.
Algebraic factors that are square values also mean the surd can be simplified.

Common misconception

Pupils may not multiply the existing coefficient with the coefficient of the simplified surd.

Replace the unsimplified surd with the simplified form within the original expression so pupils can see they need to multiply coefficients.

Keywords

Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.
Simplest form - A surd is in its simplest form when the radicand is an integer with no perfect square factors greater than 1.

Pupils may grasp this quickly and want to rush ahead. A firm understanding of the basics are needed here though as otherwise pupils may struggle as their surd manipulation skills increase.

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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Worksheet

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Starter quiz

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6 Questions

Q1.

Identify the surds.

Correct answer: $$\sqrt {xy}$$

Correct answer: $$\sqrt {60}$$

$$\sqrt {x^2}$$

$$\sqrt {36 \times 4^2}$$

Q2.

Write an equivalent expression for $$\sqrt {d^2 \times e^2 \times h^2}$$ that does not involve the radical sign.

Correct Answer: deh, $$d \times e \times h$$, dxexh, d x e x h

Q3.

True or false? $$\sqrt {41}$$ is in its simplest form.

Correct answer: True

False

Q4.

Which of these is not a square factor of 64?

Correct answer: 9

Q5.

Which of these is not a square factor of 2700?

Correct answer: 675

900

Q6.

True or false? The highest square factor of 225 is 25.

True

Correct answer: False

Exit quiz

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6 Questions

Q1.

A surd is in its simplest form when the is an integer with no perfect square factors greater than 1.

Correct Answer: radicand

Q2.

Which of these surds are in their simplest form?

Correct answer: $$4\sqrt 3$$

$$3\sqrt 8$$

$$\sqrt {64}$$

Correct answer: $$4\sqrt {21}$$

Q3.

$$\sqrt {72}$$ simplifies to $$6\sqrt a$$. What is the value of $$a$$?

Correct Answer: 2, two

Q4.

$$4\sqrt {72}$$ simplifies to $$k\sqrt 2$$. What is the value of $$k$$?

Correct answer: 24

Q5.

$$7\sqrt {48}$$ simplifies to $$h\sqrt 3$$. What is the value of $$h$$?

Correct answer: 28

Q6.

$$2\sqrt {180}$$ simplifies to $$d\sqrt 5$$. What is the value of $$d$$?

Correct answer: 12