Types of number：練習題

Which of the following is a square number?

Which of the following statements about number types is always true?

Which of the following is an irrational number?

Which of the following statements is false regarding the properties of numbers?

Which set contains only natural numbers as defined in the syllabus \((0, 1, 2, \dots)\)?

Identify the prime number from the following list of integers: \(12, 15, 17, 21\).

Calculate the square of the reciprocal of \(\frac{2}{5}\).

From the following list, identify the irrational number: \( \sqrt{9}, 0.33, \pi, \frac{4}{7} \).

The first four triangle numbers are 1, 3, 6, and 10.
(a) Write down the next two triangle numbers in this sequence.
(b) Determine whether 25 is a triangle number. Show your working or explain your reasoning.

(a) Express 150 and 225 as products of their prime factors, giving your answers in index form.
(b) Use your results to find the highest common factor (HCF) of 150 and 225.
(c) Use your results to find the lowest common multiple (LCM) of 150 and 225.