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 \(p(x)=x^2-7\), what is the value of \(p(\sqrt{7}+1)\)?HardLevel 28For which (k) will (x=\sqrt{2}) be a zero of the polynomial (x^2+kx-2)?HardLevel 28If (x=1+\sqrt{2}), what is (x+\frac{1}{x})?HardLevel 28If (x=3+\sqrt{8}), what is (\frac{1}{x}) equal to?HardLevel 28If (\alpha=\sqrt{5}+2) and (\beta=\sqrt{5}-2), what is (\alpha\beta)?HardLevel 28If (\alpha=5+\sqrt{6}) and (\beta=5-\sqrt{6}), what are (\alpha+\beta) and (\alpha\beta) respectively?HardLevel 28If (p(x)=x^2-10x+19), what are its zeroes?HardLevel 28If (x^2-6x+1=0), what type are the values of (x)?HardLevel 28If (x^2-4x+4=0), what is the nature of the roots?HardLevel 28If (x^2+2x+5=0), which statement about the roots in the real number system is correct?HardLevel 28For which value of (k) will the roots of (x^2-2kx+2=0) be irrational and real?HardLevel 26If (p(x)=2x^2-3x+\sqrt{2}), what type of polynomial is it?HardLevel 26If (p(x)=x^2-(\sqrt{3}+1)x+\sqrt{3}), what are the zeroes?HardLevel 26If (p(x)=x^2-\sqrt{5}x), what are its zeroes?HardLevel 26If x = √2 + √3, what is the correct form of x²?MediumLevel 26If (x=\sqrt{3}+\sqrt{2}), which quadratic equation does (x) satisfy?HardLevel 26If (x=2+\sqrt{5}), what is the value of (x^2-4x-1)?HardLevel 26If (x=3-\sqrt{2}), what is the value of (x^2-6x+7)?HardLevel 26If \(x=\sqrt{11}\), what is the value of \(x^4-121\)?HardLevel 26If p(x) = x³ − 2x, what is p(√2)?MediumLevel 26