Page 28 - Mathematics

4. State whether the following statements are true or false. Justify your
answers.
(a) Every irrational number is a real number.
(b) All non-terminating decimals are irrational numbers.
(c) The square roots of all positive numbers are irrational numbers.
(d) The sum of two irrational numbers gives an irrational number.
5. Ramadhani is planning to build a circular pond whose base area is 100
square metres. Express the radius of the base of the pond as an irrational
number.

6. Identify irrational numbers from the following list of numbers:
Tanzania Institute of Education
91 2 1
 
9, 0.54, , 1.256, , .
13 2 11
7. (a) What is an irrational number?
(b) Explain the fact that the sum of two or more irrational numbers
gives an irrational number.
8. Provide an example for each of the following statements.
(a) The product of rational and irrational number is an irrational number.
(b) The product of two irrational numbers is an irrational number.
9. Write five irrational numbers with denominators as irrational numbers.
10. In the following list of numbers, identify a list which does not contain
irrational numbers.
2
(a) 0.1, , 5.33333 
7
(b) 16, 1, 9, 3.844231028...

2

(c) 4, 4, 0.6, 7
9
28
(d) − , 0, 25, 3.45
9

Real numbers
Mathematics Form One numbers, whole numbers, integers, rational numbers and irrational numbers are
Real numbers are the numbers which include both rational and irrational numbers.
A set of real numbers is denoted by . Thus, all sets of numbers such as natural

all real numbers. Natural numbers are the smallest set of numbers followed by
whole numbers and integers which are all rational numbers. Rational and irrational
numbers are opposite sets of numbers and are what makes the largest set of real
numbers as shown in Figure 2.1.

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Mathematics form 1.indd 22
Mathematics form 1.indd 22 25/10/2024 09:51:06