Mathematics
Irrational numbers
अपरिमेय संख्याएँ
In this Class 9 Mathematics topic from the Number Systems chapter, students learn that irrational numbers cannot be written in the form p/q, where p and q are integers and q is not zero. They explore familiar examples such as √2 and π, understand their non-terminating, non-repeating decimal expansions, and distinguish them from rational numbers. The topic also develops skills for representing irrational numbers on the number line and understanding their place within the real number system.
Practice questions
Which statement is true for an irrational number?EasyLevel 17A student says, “The sum of two irrational numbers is always irrational.” Which of the following examples proves the statement wrong?EasyLevel 17A number has the decimal expansion \(0.101001000100001\ldots\), in which the number of zeros between successive 1s keeps increasing. What type of number is it?EasyLevel 17A student says that every non-terminating decimal is irrational. Which of the following numbers proves the statement wrong?EasyLevel 17Which is the simplified form of \((\sqrt{98})\)?EasyLevel 17What is the simplified form of (2\sqrt{6}-\sqrt{6})?EasyLevel 17If (\sqrt{a}) is irrational then which condition can be true for (a)?EasyLevel 16Riya makes two statements about irrational numbers:
Statement I: The sum of two irrational numbers is always irrational.
Statement II: The product of a non-zero rational number and an irrational number is always irrational.
Which option is correct?EasyLevel 16The side of a square is (\sqrt{7}) units. What type of number will its perimeter be?EasyLevel 18If the area of a square is (11) square units then what type of number will its side be?EasyLevel 18Which decimal form can identify an irrational number?EasyLevel 18What type of number is the decimal (2.5050050005\ldots)?EasyLevel 18Reema says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. What is the correct evaluation of Reema’s statement?EasyLevel 18Which square root is not irrational?EasyLevel 18If x = √6, what type of number is 2x?EasyLevel 18Neha says, “Every non-terminating decimal expansion is irrational.” Which of the following examples proves her statement wrong?EasyLevel 18Which number definitely lies between (\sqrt{10}) and (\sqrt{11})?EasyLevel 18A student claims that every non-terminating decimal is irrational. Which of the following numbers disproves this claim?EasyLevel 18Ravi says that \(\sqrt{49}\) is an irrational number because it has a square-root sign. Which statement correctly corrects Ravi’s error?EasyLevel 18A student says, “The decimal expansion of every irrational number is non-terminating and non-repeating.” How is this statement?EasyLevel 18