Identifying square factors to support simplifying surds | Maths

Starter quiz

True or false? The group of integers would include values like 0.27

True

False ✓
An ______ number is one that cannot be written in the form $a \over b$ where $a$ and $b$ are both integers and $b \ne 0$ .

'irrational' ✓
Identify the irrational number.

$\sqrt 0$

$\sqrt 1$

$\sqrt 7$ ✓

$\sqrt 9$
Which of these is not a surd?

$\sqrt {24}$

$\sqrt {35}$

$\sqrt {42}$

$\sqrt {49}$ ✓
Which of these is not a surd?

$\sqrt[3] {27}$ ✓

$\sqrt[3] {33}$

$\sqrt[3] {39}$

$\sqrt[3] {42}$
Which of these is not a surd?

$\sqrt {1 \over 6}$

$\sqrt {1 \over 81}$ ✓

$\sqrt {0.3}$

$\sqrt {0.95}$

Identify the surds.

$\sqrt {ab}$ ✓

$\sqrt {a^2}$

$\sqrt {16 \times 3^2}$

$\sqrt 6$ ✓
Write an equivalent expression for $\sqrt {2^4 \times 5^2}$ that does not involve the radical sign.

'20' ✓
True or false? $\sqrt {40}$ is in its simplest form.

True
False ✓
Which of these is not a square factor of 64?

1

4

16

32 ✓
Which of these is not a square factor of 2700?

9

25

64 ✓

900
True or false? The highest square factor of 108 is 9.

True
False ✓

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Pupils may not fully simplify due to not identifying the highest square factor.

Encourage pupils to check the resulting radicand for any further square factors.

Perfect square - A perfect square is a number that is the second exponent of an integer. It is usually shortened to square number.
Surd - A surd is an irrational number expressed as the root of a rational number.
Radical - The root sign is the radical symbol.
Radicand - The radicand is the value inside the radical symbol.