Multiplication of surds | Maths | Quizalize & Oak National Academy

Starter quiz

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

$\sqrt {48}$

$2\sqrt {27}$

$2\sqrt {12}$

$2\sqrt {18}$ ✓
Three of the surds are like surds. Which one is not?

$-5\sqrt {80}$

$-5\sqrt {30}$ ✓

$a\sqrt {20}$

$b\sqrt {45}$
$10\sqrt {3} + a\sqrt {3} = -3\sqrt {3}$ . What is the value of $a$ ?

'-13' ✓
Simplify the expression $\sqrt {12} + \sqrt {3} - \sqrt {27}$

$3\sqrt {3} - \sqrt {27}$

$-4\sqrt {3}$

$6\sqrt {3}$

0 ✓
True or false? $\sqrt {20}$ and $\sqrt {45}$ are like terms.

True
False ✓
Simplify the expression $2\sqrt {15} + 3\sqrt {20} - 7\sqrt {80}$

$2\sqrt {15} - 100\sqrt {5}$

$2\sqrt {15} - 22\sqrt {5}$ ✓

$2\sqrt {15} - 4\sqrt {5}$

$2\sqrt {15} - 2\sqrt {5}$

Calculate $\sqrt {99} \times \sqrt {99}$

'99' ✓
Calculate $\sqrt {3.9} \times \sqrt {3.9}$

'3.9' ✓
When multiplying surds, we ______ the radicands.

'multiply' ✓
Match up the multiplications with the simplied answers.

$2\sqrt {6}$

⇔

$\sqrt {6} \times \sqrt {4}$ ✓

30

⇔

$3\sqrt {10}\times \sqrt {10}$ ✓

$7\sqrt {2}$

⇔

$\sqrt {14} \times \sqrt {7}$ ✓

$3\sqrt {2}$

⇔

$\sqrt {3} \times \sqrt {6}$ ✓
When dividing surds we ______ the radicands.

'divide' ✓
Simplify the following expression: $\sqrt {12} \div \sqrt {3}$

'2' ✓

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The square root operation is equivalent to the exponent 0.5 where the base is the term under the square root.
You can deduce this as squaring and square rooting are inverse operations.
Since the exponents for each term are the same, they can be combined.

Pupils may not simplify after multiplying surds.

Surds should always be written in their simplest form for the final answer.

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.