Mathematics
Irrational numbers and real numbers
अपरिमेय संख्याएँ और वास्तविक संख्याएँ
In this Class 10 Mathematics topic, students build a clear understanding of real numbers as the collection of rational and irrational numbers. They learn to identify irrational numbers, compare and represent real numbers on the number line, and interpret terminating, recurring, and non-terminating non-recurring decimals. The topic also develops confidence with properties and operations involving real numbers, providing useful foundations for reading polynomial expressions, coefficients, and real zeros in the surrounding Polynomials chapter.
Practice questions
If an irrational number is to be chosen between (\sqrt{2}) and (\sqrt{3}), which option is definitely correct?ExpertLevel 26If (x=5+2\sqrt{6}), which quadratic polynomial with rational coefficients can have (x) as a zero?ExpertLevel 26If the zeroes of (p(x)=x^2-6x+k) are (3+\sqrt{2}) and (3-\sqrt{2}), what is the value of (k)?ExpertLevel 26What is the rationalized form of (\frac{2}{\sqrt{11}-3})?ExpertLevel 26If (x=\sqrt{13}+\sqrt{12}), then (\frac{1}{x}) is equal to which expression?ExpertLevel 26If (\frac{154}{2\cdot5^2\cdot7\cdot11}) is written in lowest form, what type of decimal expansion will it have?ExpertLevel 26In which option is the sum of (\sqrt{3}) and (\sqrt{12}) correctly written as a simple irrational form with rational coefficient?ExpertLevel 26If one zero of a quadratic polynomial with rational coefficients is (4+\sqrt{11}), what will be the other zero?ExpertLevel 27Which quadratic polynomial has zeros \(2+\sqrt{10}\) and \(2-\sqrt{10}\)?ExpertLevel 27If \(x=\sqrt{7}+\sqrt{5}\), what is the value of \(x^2\)?ExpertLevel 27Which expression is a rational number?ExpertLevel 27If (p) and (q) are non-zero rational numbers and (p+q\sqrt{3}=0), which conclusion is correct?ExpertLevel 27If \(a=\sqrt{13}+\sqrt{6}\) and \(b=\sqrt{13}-\sqrt{6}\), what is the value of \(ab\)?ExpertLevel 27What is the rationalized form of (\frac{3}{\sqrt{13}-2})?ExpertLevel 27If \(x=4-\sqrt{15}\), then \(\frac{1}{x}\) is equal to which expression?ExpertLevel 27If the zeroes are 6 + √5 and 6 − √5, what are their sum and product respectively?MediumLevel 27In which option is the product of two irrational numbers rational?ExpertLevel 27If (\sqrt{5}) is assumed to be (\frac{p}{q}) where (p) and (q) are coprime, what creates the contradiction?ExpertLevel 27If (p(x)=x^2-8x+13), what are its zeroes?ExpertLevel 27What is the simplified form of (\sqrt{27}+\sqrt{75}-\sqrt{12})?ExpertLevel 27