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 p(x)=x²−2x−3√2, what does the constant term tell about the zeroes?MediumLevel 25If p(x)=x²−6√2x+17, what are the sum and product of its zeroes?MediumLevel 25If \(p(x)=x^2-6\sqrt{2}x+17\), what is the difference between its zeroes?ExpertLevel 25If the zeroes of (x^2-Sx+P) are (2\sqrt{3}+1) and (2\sqrt{3}-1), what are (S) and (P)?ExpertLevel 25Which option can form a quadratic polynomial with rational coefficients?ExpertLevel 25If (p(x)=x^2-2x-2), what is (p(1+\sqrt{3}))?ExpertLevel 25If (p(x)=x^2-2x-2), which statement about (1+\sqrt{3}) is correct?ExpertLevel 25If one zero of (p(x)=x^2-2x-2) is (1+\sqrt{3}), what is the other zero?ExpertLevel 25If the zeroes of a monic quadratic polynomial are \(a+\sqrt{b}\) and \(a-\sqrt{b}\), what is its discriminant?ExpertLevel 25If (\alpha=4+\sqrt{15}) and (\beta=4-\sqrt{15}), what is the value of (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?ExpertLevel 25If (\sqrt{2}+x) is a rational number and (x) is a real number, which statement about (x) is definitely true?HardLevel 28If (a) is rational and (a\ne0), what type of number is (a\sqrt{5})?HardLevel 28Which of the following numbers is definitely rational?HardLevel 28Which option is actually a rational number?HardLevel 28If (p(x)=x^2-5x+6), what type of number is (p(\sqrt{2}))?HardLevel 28If (2+\sqrt{3}) is a zero of the polynomial (x^2-4x+1), what is the other zero?HardLevel 28If the zeroes of a quadratic polynomial are \(3+\sqrt{5}\) and \(3-\sqrt{5}\), what is their sum?HardLevel 28If the zeroes of a quadratic polynomial are \(4+\sqrt{7}\) and \(4-\sqrt{7}\), what is their product?HardLevel 28Which monic quadratic polynomial has zeroes (2+\sqrt{6}) and (2-\sqrt{6})?HardLevel 28If x = √3, what is the value of x² − 3?EasyLevel 28