Addition with surds | Maths | Quizalize & Oak National Academy

Starter quiz

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

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

$3\sqrt 4$

$8\sqrt 3$ ✓

$\sqrt {100}$

$21\sqrt 9$
$\sqrt {18}$ simplifies to $a\sqrt 2$ . What is the value of $a$ ?

'3' ✓
$3\sqrt {76}$ simplifies to $k\sqrt {19}$ . What is the value of $k$ ?

2

3

6 ✓

19
$3\sqrt {125}$ simplifies to $h\sqrt 5$ . What is the value of $h$ ?

'15' ✓
$9\sqrt {98}$ simplifies to $d\sqrt 2$ . What is the value of $d$ ?

'63' ✓

Three of the surds are like surds. Which one is not?

$-5\sqrt 2$

${4 \over 5}\sqrt 2$

$b\sqrt 2$

$5\sqrt {22}$ ✓
Three of the surds are like surds. Which one is not?

$a\sqrt 5$

${2 \over 3}\sqrt 5$

$a\sqrt {20}$

$-5\sqrt {30}$ ✓
$4\sqrt {6} - a\sqrt {6} = -5\sqrt {6}$ . What is the value of $a$ ?

'9' ✓
After gathering like terms in the expression $4 - 3\sqrt b + 7\sqrt {bc} + 3\sqrt b - 20 - \sqrt {bc}$ , how many terms will be in the resulting expression?

'2' ✓
Is the statement "It is always best to simplify before adding surds"

Always true

Sometimes true ✓

Never true
Calculate the perimeter of a square with side length $\sqrt {18} + \sqrt {20}$ . Give your answer as simply as possible.

$4\sqrt {18} + 4\sqrt {20}$

$8\sqrt {5} + 12\sqrt {2}$ ✓

$4(\sqrt {18} + \sqrt {20})$

$3\sqrt {2} + 2\sqrt {5}$

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Pupils may think like surds need both the radicand and the coefficient to be the same.

Remind them of the distributive law: a(b+c) = ab + ac.

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.