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 \(a=\sqrt{7}+\sqrt{2}\) and \(b=\sqrt{7}-\sqrt{2}\), what is the value of \(ab\)?HardLevel 25Which option is the value of (\frac{\sqrt{3}}{\sqrt{12}})?HardLevel 25Which option correctly compares (\sqrt{2}+\sqrt{3}) and (\sqrt{5})?HardLevel 25Which of the following is a rational number between \(\sqrt{99}\) and \(\sqrt{100}\)?HardLevel 25Which option is the simplified form of (4\sqrt{7}+2\sqrt{28}-\sqrt{175})?HardLevel 25If \(x=\sqrt{3}+\sqrt{2}\), what is the value of \(x^2-5\)?HardLevel 25Which option is the rationalized form of (\frac{1}{5-\sqrt{6}})?HardLevel 25Which option is the value of (\sqrt{2}\times(\sqrt{18}-\sqrt{8}))?EasyLevel 25Which option is the simplified form of (\sqrt{5}+\sqrt{20}+\sqrt{45}+\sqrt{80})?HardLevel 25Which of the following is the simplified form of \(\sqrt{10+\sqrt{96}}\)?HardLevel 25If \(x=\sqrt{7}+\sqrt{3}\), what is the value of \(x^2-10\)?HardLevel 25If (p(x)=x^2-2), which statement about its real zeroes is correct?HardLevel 28If a quadratic polynomial has rational coefficients and one zero is (3+\sqrt{5}), what will be the other zero?HardLevel 28Which of the following linear polynomials has zero \(2\sqrt{3}\)?HardLevel 28If (p(x)=x^2-6x+4), what is the nature of its zeroes?HardLevel 28Which polynomial has zeros \\(\\sqrt{7}\\) and \\(-\\sqrt{7}\\)?HardLevel 28If \(2+\sqrt{3}\) and \(2-\sqrt{3}\) are zeroes of a quadratic polynomial, what is the polynomial?HardLevel 28If the zeros of \(p(x)=x^2-kx+1\) are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), what is the value of \(k\)?HardLevel 28If \(p(x)=x^2-2\sqrt{5}x+5\), which statement about its zeroes is correct?HardLevel 28For which value of k will \(p(x)=x^2-10x+k\) have zeros \(5+\sqrt{2}\) and \(5-\sqrt{2}\)?HardLevel 28