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Solving equations with surds

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Lesson details

Learning outcome

I can solve an equation where some of the coefficients or terms are surds.

Key learning points

  1. A surd is a value, not a variable.
  2. Your knowledge of surds can be used alongside your knowledge of algebraic manipulation.

Keywords

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

Common misconception

Pupils may want to write rounded solutions when solving a quadratic equation.

Remind them of the importance of accuracy and further calculations.

Teacher tip

Pupils may have scientific calculators which allow them to solve quadratic equations. They can check their working using this tool (or by using software) should they wish. Ask them to reflect on the form the solutions are given in.

Licence

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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Prior knowledge starter quiz

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6 Questions

Q1.
Solve the equation $$3(x+12) = 36$$

Correct Answer: 0, x = 0

Q2.
Solve the equation $$2(3x - 10) - 3(7 - 5x) = 484$$

Correct Answer: 25, x = 25

Q3.
$$x^{2} + 2bx + c = (x + b)^{2} - b^{2} + c$$ is known as completing the .

Correct Answer: square

Q4.
Select the correct form for the quadratic formula.

$$x = {b \pm \sqrt{b^2-4ac} \over 2a}$$
$$x = {-b \pm \sqrt{b^2+4ac} \over 2a}$$
$$x = {-b \pm \sqrt{b^2-4ac} \over 2}$$
Correct answer: $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

Q5.
Simplify the expression: $$\sqrt {12} \times \sqrt {30}$$

Correct answer: $$6\sqrt {10}$$
$$2/5$$
$$2\sqrt {3} \times 3\sqrt {10}$$
6

Q6.
$$\sqrt {54} \times \sqrt {24}$$

Correct Answer: 36, thirty six

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
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

Q2.
Solve $$x\sqrt {180} - 30 = x\sqrt {80}$$ and write your answer in the form $$a\sqrt {b}$$. State the value of $$a$$.

Correct Answer: 3

Q3.
True or false? The solutions to $$2x^{2} + 9x - 2 = 0$$ are $$x = -9 \pm \sqrt {97}$$

True
Correct answer: False

Q4.
Match the equation to its solutions

Correct Answer:$$x^{2} + 9x - 2 = 0$$,$$x = {{-9 \pm \sqrt {89}} \over {2}}$$

$$x = {{-9 \pm \sqrt {89}} \over {2}}$$

Correct Answer:$$x^{2} + 4x - 2 = 0$$,$$x = -2 \pm \sqrt {6}$$

$$x = -2 \pm \sqrt {6}$$

Correct Answer:$$2x^{2} + 5x - 2 = 0$$,$$x = {{-5 \pm \sqrt {41}} \over {4}}$$

$$x = {{-5 \pm \sqrt {41}} \over {4}}$$

Correct Answer:$$2x^{2} + 3x - 8 = 0$$,$$x = {{-3 \pm \sqrt {73}} \over {4}}$$

$$x = {{-3 \pm \sqrt {73}} \over {4}}$$

Q5.
True or false? The solutions to $$x^{2} + 5x - 4 = 0$$ are $$x = \frac{1}{2} (-5 \pm \sqrt {41})$$

Correct answer: True
False

Q6.
Is this statement true or false? "There are always two solutions to a quadratic equation"

Correct answer: False
True

To help you plan your 10 maths lesson on: Solving equations with surds, download all teaching resources for free and adapt to suit your pupils' needs...