Rational and Irrational Numbers: math test, Grade 8 – download the PDF

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7 October 20267 October 2026

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Math tests Grade 8 : Rational and Irrational Numbers — Zyro the alien explorer of Planète Maths

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

1 Classify the numbers / 4 pts

Calculator not allowed. Classify each number as rational or irrational: \(-\dfrac{9}{4}\), \(\sqrt{64}\), \(\sqrt{45}\), \(0.\overline{27}\), \(5\pi\), \(0.3030030003\ldots\) (one more zero each time). Then explain in one sentence why \(\sqrt{45}\) is not an integer.

2 Repeating decimals / 4 pts

Write as fractions in lowest terms, showing the subtraction: a) \(0.\overline{15}\) b) \(0.7\overline{2}\)

3 Roots and equations / 4 pts

Calculator not allowed. a) \(\sqrt{169}\) b) \(\sqrt[3]{-216}\) c) \(\sqrt{\dfrac{49}{64}}\) d) Solve \(x^2 = 121\). e) Solve \(x^3 = 0.027\).

4 Estimating a root / 3 pts

a) Between which two consecutive integers is \(\sqrt{57}\)? b) Use squares to decide whether \(\sqrt{57}\), rounded to the nearest tenth, is \(7.5\) or \(7.6\).

5 Order the numbers / 3 pts

Calculator allowed. Order from least to greatest: \(-\sqrt{10}\), \(-3.2\), \(-\pi\), \(-\dfrac{10}{3}\), \(-3.1\).

6 The rug / 2 pts

Calculator allowed. A square rug has an area of \(30\) square feet. a) Find its side length to the nearest tenth of a foot. b) Is the exact side length rational or irrational? Explain.