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
Which quadratic polynomial has zeroes (3+\sqrt{2}) and (3-\sqrt{2})?ExpertLevel 26If x = \sqrt{6} + \sqrt{2}, what is the value of x^2?ExpertLevel 26If (\frac{a}{b}) is in lowest form and (b=2^4\cdot5^3\cdot7), what type of decimal expansion will it have?ExpertLevel 26Which fraction will have a terminating decimal expansion?ExpertLevel 26If \(a=\sqrt{11}+\sqrt{5}\) and \(b=\sqrt{11}-\sqrt{5}\), what is the value of \(ab\)?ExpertLevel 26If (3+\sqrt{2}) and (3-\sqrt{2}) are zeroes of a polynomial, what is the sum of the zeroes?ExpertLevel 26Which number, when squared, equals (7+4\sqrt{3})?ExpertLevel 26If (\sqrt{m}) is irrational and (m) is a positive integer, which conclusion about (m) is correct?ExpertLevel 26If (x=2-\sqrt{3}), then (\frac{1}{x}) is equal to which expression?ExpertLevel 26In which option is the sum of a rational and an irrational number irrational?ExpertLevel 26In which option is the sum of two irrational numbers rational?ExpertLevel 26If (\sqrt{3}) is assumed rational and written as (\sqrt{3}=\frac{p}{q}), where (p) and (q) are coprime, where does the contradiction arise?ExpertLevel 26Which polynomial has (1+\sqrt{6}) and (1-\sqrt{6}) as zeroes?ExpertLevel 26If (p(x)=x^2-4x-1), what are its zeroes?ExpertLevel 26Which option is not a real number?ExpertLevel 26If (x=3+\sqrt{10}), what is the value of (x+\frac{1}{x})?ExpertLevel 26If (\alpha=4+\sqrt{15}) and (\beta=4-\sqrt{15}), what is (\alpha+\beta+\alpha\beta)?ExpertLevel 26If (\frac{35}{2^2\cdot5\cdot7^2}) is written in lowest form, what type of decimal expansion will it have?ExpertLevel 26Which expression is not a rational number?ExpertLevel 26If \(x=\sqrt{7}-\sqrt{3}\), what is \(x^2\)?ExpertLevel 26