Solving equations with surds | Maths | Quizalize & Oak National Academy

Starter quiz

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

'0' ✓
Solve the equation $2(3x - 10) - 3(7 - 5x) = 484$

'25' ✓
$x^{2} + 2bx + c = (x + b)^{2} - b^{2} + c$ is known as completing the ______ .

'square' ✓
Select the correct form for the quadratic formula.

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

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

$x = {-b \pm \sqrt{b^2-4ac} \over 2}$

$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$ ✓
Simplify the expression: $\sqrt {12} \times \sqrt {30}$

$6\sqrt {10}$ ✓

$2/5$

$2\sqrt {3} \times 3\sqrt {10}$

6
$\sqrt {54} \times \sqrt {24}$

'36' ✓

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

'5' ✓
Solve $x\sqrt {180} - 30 = x\sqrt {80}$ and write your answer in the form $a\sqrt {b}$ . State the value of $a$ .

'3' ✓
True or false? The solutions to $2x^{2} + 9x - 2 = 0$ are $x = -9 \pm \sqrt {97}$

True
False ✓
Match the equation to its solutions

$x^{2} + 9x - 2 = 0$

⇔

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

$x^{2} + 4x - 2 = 0$

⇔

$x = -2 \pm \sqrt {6}$ ✓

$2x^{2} + 5x - 2 = 0$

⇔

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

$2x^{2} + 3x - 8 = 0$

⇔

$x = {{-3 \pm \sqrt {73}} \over {4}}$ ✓
True or false? The solutions to $x^{2} + 5x - 4 = 0$ are $x = \frac{1}{2} (-5 \pm \sqrt {41})$

True ✓
False
Is this statement true or false? "There are always two solutions to a quadratic equation"

False ✓
True

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

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

Remind them of the importance of accuracy and further calculations.

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