Online Test — Irrational Numbers
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
Which of the following is an irrational number?
\(\frac{3}{4}\)
\(\sqrt{9}\)
\(\sqrt{7}\)
0.25
Explanation: \(\sqrt{7}\) cannot be written as a fraction; \(\sqrt{9}=3\) is rational
Question 2 of 10
The decimal expansion of \(\sqrt{3}\) is:
Terminating
Repeating
Non-terminating non-repeating
Terminating and repeating
Explanation: Square roots of non-perfect squares are irrational → non-terminating non-repeating
Question 3 of 10
Which of the following is rational?
\(\pi\)
\(\sqrt{2}\)
\(0.1010010001...\)
\(\sqrt{16}\)
Explanation: \(\sqrt{16}=4\), which is an integer (rational)
Question 4 of 10
Between which two integers does \(\sqrt{15}\) lie?
2 and 3
3 and 4
4 and 5
5 and 6
Explanation: \(3^2=9\), \(4^2=16\), and \(9<15<16\)
Question 5 of 10
The number \(3.1415926535...\) is:
Rational
Irrational
Integer
Natural
Explanation: This is \(\pi\), which has non-repeating decimal expansion
Question 6 of 10
Which is the correct approximation of \(\sqrt{2}\) to two decimal places?
1.41
1.42
1.40
1.44
Explanation: \(1.41^2=1.9881\), \(1.42^2=2.0164\); 1.41 is closer
Question 7 of 10
The sum of a rational and an irrational number is:
Always rational
Always irrational
Sometimes rational
Always zero
Explanation: Example: \(2 + \sqrt{2}\) is irrational
Question 8 of 10
Which of these has a terminating decimal expansion?
\(\frac{1}{3}\)
\(\frac{1}{6}\)
\(\frac{1}{8}\)
\(\frac{1}{7}\)
Explanation: \(1/8 = 0.125\) (ends); others repeat
Question 9 of 10
\(\sqrt{50}\) lies between:
5 and 6
6 and 7
7 and 8
8 and 9
Explanation: \(7^2=49\), \(8^2=64\), and \(49<50<64\)
Question 10 of 10
Which method is used to geometrically construct irrational numbers on a number line?
Pythagoras theorem
Archimedes principle
Euclid's algorithm
Binomial theorem
Explanation: Pythagorean theorem (\(a^2+b^2=c^2\)) is used to construct \(\sqrt{n}\)