Rationalising a single term denominator | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these fractions are written in simplest form?

${1.2} \over {2.4}$

${3} \over {5}$ ✓

${39} \over {102}$

${0.2} \over {10}$
Evaluate $\sqrt {41} \times \sqrt {41}$

'41' ✓
Evaluate $\sqrt {0.3999} \times \sqrt {0.3999}$

'0.3999' ✓
If the radicand is rational, then squaring the surd results in a ______ number.

'rational' ✓
Evaluate $(\sqrt {42})^2$

'42' ✓
True or false? An equivalent fraction can be created by multiplying the denominator by the scale factor.

True
False ✓

True or false? $\sqrt {7 {1\over9}}$ is in its simplest form.

True
False ✓
Simplify $\sqrt {30 {1\over4}}$ . Write your answer in decimal notation.

'5.5' ✓
What should you multiply by to rationalise $5 \over \sqrt {5}$ ?

$5 \over \sqrt {5}$

$1 \over \sqrt {5}$

$sqrt {5}$

$\sqrt {5} \over \sqrt {5}$ ✓
What should you multiply by to rationalise ${3 + 2\sqrt {3}} \over \sqrt {7}$ ?

${\sqrt {7}} \over {\sqrt {7}}$ ✓

${\sqrt {3}} \over {\sqrt {3}}$

${3 + 2\sqrt {3}} \over \sqrt {7}$

${3 + 2\sqrt {3}} \over {3 + 2\sqrt {3}}$
Rationalise the denominator ${3\sqrt {3}} \over {2\sqrt {2}}$

${{27} \over {8}}$

${{6\sqrt {6}} \over {8}}$

${{3\sqrt {6}} \over {4}}$ ✓

${{27} \over {6 \sqrt {6}}}$
Rationalise the denominator ${36} \over {3\sqrt {4}}$

'6' ✓

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Fractions should be given in their simplest term.
The denominator should be written as simply as possible.
Using equivalent fractions, you may be able to write the denominator without a surd.

Pupils may think the simplest form means a simplified surd as a denominator.

A fraction is not fully simplified if the denominator contains a surd term and must be rationalised as is convention.

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