Number 10

3 marks · Normal

Is the number rational or irrational? Explain how you know, using what you know about rational and irrational numbers.

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Irrational. cannot be written as a fraction of two integers, because 15 is not a perfect square. The decimal expansion never terminates or repeats.

Must show: States is irrational, Explains it cannot be written as a fraction of integers, Refers to 15 not being a perfect square OR infinite, non-repeating decimal

Also accept: Cites non-terminating, non-repeating decimal as explanation

Common mistakes: States it is rational because it is a root; Does not link reasoning to definition

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Marking points

B1 · 1 mark · Identifies correctly that is irrational.

M1 · 1 mark · States or demonstrates that cannot be written as a fraction of two integers.

M2 · 1 mark · Gives a valid reason: 15 is not a perfect square, or explains about non-terminating non-repeating decimal.

Worked solution

The number is irrational, because 15 is not a perfect square, so cannot be written as a fraction of two integers. Its decimal expansion continues forever without terminating or repeating.