Problem solving with surds | Maths | Quizalize & Oak National Academy

Starter quiz

Order the fractions from smallest to largest.

1

⇔

$2 \over 7$

2

⇔

$1 \over 3$

3

⇔

$4 \over 9$

4

⇔

$3 \over 5$

5

⇔

$5 \over 8$
What is the value of $a + b - c$ when $a$ = 7, $b$ = 21 and $c$ = 2.4

'25.6' ✓
In order to rationalise $(2 - \sqrt {3})$ you would multiply by:

$(2 + \sqrt {3})$ ✓

$(-2 + \sqrt {3})$

$(3 - \sqrt {2})$

$(3 + \sqrt {2})$
True or false? Pythagoras' theorem can only be used to find the length of the hypotenuse.

True
False ✓
When is a surd in it's simplest form?

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

'5' ✓

True or false? Surds are a way of giving an answer exactly.

True ✓
False
Arrange the surds from smallest to largest.

1

⇔

$1 \over \sqrt {5}$

2

⇔

$2 \over \sqrt {7}$

3

⇔

$\sqrt {3}$

4

⇔

$\sqrt {7}$
The perimeter of a rectangle is $12 + 8\sqrt {2}$ . One of the lengths is $6 + \sqrt {2}$ . Find the area.

$10\sqrt {2}$

$20 + 60\sqrt {2}$

$3\sqrt {2}$

$6 + 18\sqrt {2}$ ✓
The length of the line between (3,8) and (7,13) can be written in the form $\sqrt {a}$ . What is the value of $a$ ?

'41' ✓
Which of these shapes has a greater area?

Shape A

Shape B ✓

They both have the same area
Which of these shapes has a greater perimeter?

Shape A

Shape B

They both have an equal perimeter ✓

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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.

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