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Year 10
Higher

Problem solving with surds

I can use my knowledge of surds to solve problems.

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New
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Year 10
Higher

Problem solving with surds

I can use my knowledge of surds to solve problems.

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Share activities with pupils
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Lesson details

Key learning points

  1. Surds are a useful format to leave an answer as.
  2. Surds can help with the accuracy of future calculations.
  3. Surds can be seen in many areas of maths.

Keywords

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

Common misconception

Pupils may be uncertain how to solve problems with surds.

Many problems can be solved through reasoning what you know, such as fully simplifying a surd.

This lesson brings together previous learning from other units and asks pupils to use their new knowledge of surds within their previous learning. Pythagoras' theorem is a useful context as it prepares pupils for 3D problems.
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This content is © Oak National Academy Limited (2025), 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.
Order the fractions from smallest to largest.
1 - $$2 \over 7$$
2 - $$1 \over 3$$
3 - $$4 \over 9$$
4 - $$3 \over 5$$
5 - $$5 \over 8$$
Q2.
What is the value of $$a + b - c$$ when $$a$$ = 7, $$b$$ = 21 and $$c$$ = 2.4
Correct Answer: 25.6
Q3.
In order to rationalise $$(2 - \sqrt {3})$$ you would multiply by:
Correct answer: $$(2 + \sqrt {3})$$
$$(-2 + \sqrt {3})$$
$$(3 - \sqrt {2})$$
$$(3 + \sqrt {2})$$
Q4.
True or false? Pythagoras' theorem can only be used to find the length of the hypotenuse.
True
Correct answer: False
Q5.
When is a surd in it's simplest form?
Correct answer: when the radicand is an integer and has no perfect square factors greater than 1
when the radicand is an integer
when the radicand is a perfect square
Q6.
Solve $$x\sqrt {180} - 30 = x\sqrt {80}$$ and write your answer in the form $$a\sqrt {b}$$. State the value of $$b$$.
Correct Answer: 5

Exit quiz

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6 Questions

Q1.
True or false? Surds are a way of giving an answer exactly.
Correct answer: True
False
Q2.
Arrange the surds from smallest to largest.
1 - $$1 \over \sqrt {5}$$
2 - $$2 \over \sqrt {7}$$
3 - $$\sqrt {3}$$
4 - $$\sqrt {7}$$
Q3.
The perimeter of a rectangle is $$12 + 8\sqrt {2}$$. One of the lengths is $$6 + \sqrt {2}$$. Find the area.
$$10\sqrt {2}$$
$$20 + 60\sqrt {2}$$
$$3\sqrt {2}$$
Correct answer: $$6 + 18\sqrt {2}$$
Q4.
The length of the line between (3,8) and (7,13) can be written in the form $$\sqrt {a}$$. What is the value of $$a$$?
Correct Answer: 41
Q5.
Which of these shapes has a greater area?
An image in a quiz
Shape A
Correct answer: Shape B
They both have the same area
Q6.
Which of these shapes has a greater perimeter?
An image in a quiz
Shape A
Shape B
Correct answer: They both have an equal perimeter