Simplifying surds | Maths | Quizalize & Oak National Academy

Starter quiz

Identify the surds.

$\sqrt {xy}$ ✓

$\sqrt {60}$ ✓

$\sqrt {x^2}$

$\sqrt {36 \times 4^2}$
Write an equivalent expression for $\sqrt {d^2 \times e^2 \times h^2}$ that does not involve the radical sign.

'deh' ✓
True or false? $\sqrt {41}$ is in its simplest form.

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

1

4

9 ✓

16
Which of these is not a square factor of 2700?

9

25

675 ✓

900
True or false? The highest square factor of 225 is 25.

True
False ✓

A surd is in its simplest form when the ______ is an integer with no perfect square factors greater than 1.

'radicand' ✓
Which of these surds are in their simplest form?

$4\sqrt 3$ ✓

$3\sqrt 8$

$\sqrt {64}$

$4\sqrt {21}$ ✓
$\sqrt {72}$ simplifies to $6\sqrt a$ . What is the value of $a$ ?

'2' ✓
$4\sqrt {72}$ simplifies to $k\sqrt 2$ . What is the value of $k$ ?

4

6

24 ✓

36
$7\sqrt {48}$ simplifies to $h\sqrt 3$ . What is the value of $h$ ?

4

7

16

28 ✓
$2\sqrt {180}$ simplifies to $d\sqrt 5$ . What is the value of $d$ ?

2

5

6

12 ✓

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The radicand should be as small as possible.
If any of the radicand's factors are square numbers then the surd can be simplified.
Algebraic factors that are square values also mean the surd can be simplified.

Pupils may not multiply the existing coefficient with the coefficient of the simplified surd.

Replace the unsimplified surd with the simplified form within the original expression so pupils can see they need to multiply coefficients.

Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.
Simplest form - A surd is in its simplest form when the radicand is an integer with no perfect square factors greater than 1.