Number Systems

Practice Questions in Irrational numbers, real numbers, exponents
  1. Prime Factorise & Rationalise Denominator

    \\frac{14}{{\sqrt {108}} - {\sqrt {96}} + {\sqrt {192}} - {\sqrt {54}}}\\)

  2. Rational numbers - Fractions

    Find 5 rational numbers between \\frac{3}{4}) and \\frac{4}{5}).

  3. Express as Fractions

    Express 1.363636... in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

  4. Express in the form \\frac{p}{q})

    Express 0.4323232… in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

  5. Simplify the following

    (a) \({8 + \sqrt{5})}) \({8 - \sqrt{5})})

    (b) \({10 + \sqrt{3})}) \({6 + \sqrt{2})})

    (c) \{(\sqrt {3} + \sqrt {11})}^2) + \{(\sqrt {3} - \sqrt {11})}^2)

  6. Rationalize the denominator:

    (a) \\frac{2}{\sqrt{3} - 1})

    (b) \\frac{7}{\sqrt{12} - \sqrt{5}})

    (c) \\frac{1}{8 + 3\sqrt{5}})

    (d) \\frac{1}{4 + \sqrt{2} + \sqrt{5}})

  7. Simplify and find the value of

    (a) \{(729)}^{\frac{1}{6}})

    (b) \{(64)}^{\frac{2}{3}})

    (c) \{(243)}^{\frac{6}{5}})

    (d) \{(21)}^{\frac{3}{2}} \times {(21)}^{\frac{5}{2}})

    (e) \\frac{{(81)}^{\frac{1}{3}}}{{(81)}^{\frac{1}{12}}})

  8. Operation on real numbers & Algebraic identities

    If x = \\frac{3 - {\sqrt{13}}}{2}\\), what is the value of \x^2 + \frac{1}{x^2}\\)?

  9. Rationalise & find value of cubic expression

    If x = \\frac{1}{8-\sqrt{60}}\\), what is the value of \x^{3}-5x^{2}+8x-4?\\)

  10. Rationalise the denominator

    \\frac{1}{9 + {\sqrt{5} + \sqrt{6}}}\\)

Video Explanation

Video Explanation

Video Explanation

Video Explanation

Video Explanation

Video Explanation

Video Explanation

Video Explanation

Video Explanation

Video Explanation