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Year 10
Higher

Solving equations with surds

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

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New
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Year 10
Higher

Solving equations with surds

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

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Lesson details

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.

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.
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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).

Lesson video

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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

Exit quiz

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

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

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

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

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

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

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

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

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