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^3-3x), what is (p(\sqrt{3}))?HardLevel 26If (x=\sqrt{2}) is a zero of (ax^2+bx+c) and (a,b,c) are rational, which conclusion cannot be correct?HardLevel 26If (\sqrt{m}) is rational and (m) is a positive integer, what is true about (m)?HardLevel 26For which value of (n) is (\sqrt{n}) irrational?HardLevel 26If (\sqrt{a}+\sqrt{b}) is rational and (a,b) are distinct prime numbers, which conclusion is correct?HardLevel 26If \(a=\sqrt{2}+\sqrt{8}\), what is the simplified form of \(a\) and what type of number is it?HardLevel 26If (a=\sqrt{27}-\sqrt{12}), what is the value of (a)?HardLevel 26If \(x=\sqrt{6}+\sqrt{2}\) and \(y=\sqrt{6}-\sqrt{2}\), what is the value of \(xy\)?HardLevel 26If (x=\frac{1}{\sqrt{5}-2}), what is the simplified form of (x)?HardLevel 26If (x=\frac{2}{\sqrt{3}+1}), what is (x) equal to?HardLevel 26If (x=\sqrt{2}) and (y=\sqrt{8}), what is the simplified ratio (x:y)?HardLevel 26Which option gives a number that is real but not rational?HardLevel 26If \(x=\sqrt{3}\), what is the value of \(2x^2-x-6\)?HardLevel 26If (x=1-\sqrt{5}), what is the value of (x^2-2x-4)?HardLevel 26Which statement is correct about the decimal expansion of (\frac{91}{2^3\cdot5^2\cdot13})?HardLevel 28If (p) and (q) are non-zero rational numbers and (p+q\sqrt{2}=0), which conclusion is correct?HardLevel 28If (a=7+4\sqrt{3}) and (b=7-4\sqrt{3}), then what type of number is (ab)?HardLevel 28One zero of a quadratic polynomial with rational coefficients is (3-\sqrt{5}). What will be the other zero?HardLevel 28If (p(x)) is a quadratic polynomial with rational coefficients and one zero is (2+\sqrt{7}), what will be the other zero?ExpertLevel 26If the zeros of a quadratic polynomial are \(5+\sqrt{3}\) and \(5-\sqrt{3}\), what is their product?ExpertLevel 26