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Year 10
Higher

Problem solving with surds

You can use your knowledge of surds to solve problems.

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New
New
Year 10
Higher

Problem solving with surds

You can use your knowledge of surds to solve problems.

Download all resources
Share activities with pupils

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.

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.

Keywords

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

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.
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.
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