1. State whether the following statements are true or false. Justify your answers.
  1. Every irrational number is a real number. True, since collection of real numbers is made up of rational and irrational numbers.
  2. Every point on the number line is of the form \(\sqrt{m}\) , where m is a natural number. False, no negative number can be the square root of any natural number.
  3. Every real number is an irrational number. False, for example 2 is real but not irrational.

2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.False, Squre root of 4 is 2 which is a rational number.

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    Frequently Asked Questions

    A number system is a way of expressing numbers using symbols and rules. It includes natural numbers, whole numbers, integers, rational, and irrational numbers.

    Real numbers include both rational and irrational numbers that can be represented on the number line.

    Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and \(q \neq 0.\)

    Irrational numbers cannot be written as a simple fraction and have non-terminating, non-repeating decimals, like v2 or p.

    Rational numbers can be expressed as p/q, while irrational numbers cannot. Rational decimals terminate or repeat; irrational decimals do not.

    Natural numbers are counting numbers starting from 1, 2, 3, and so on.

    Whole numbers include all natural numbers and 0, i.e., 0, 1, 2, 3, 4, ...

    Integers include all whole numbers and their negatives, such as … -3, -2, -1, 0, 1, 2, 3 …

    The decimal expansion of rational numbers is either terminating or non-terminating repeating.

    The decimal expansion of irrational numbers is non-terminating and non-repeating.

    Yes, every real number, whether rational or irrational, can be represented on the number line.

    All rational numbers are real, but not all real numbers are rational. Real numbers include both rational and irrational types.

    Construct a right-angled triangle with both legs of 1 unit each; the hypotenuse represents v2 when plotted on the number line.

    A non-terminating decimal continues infinitely without ending, like 0.333... or 0.142857142857...

    A repeating decimal has digits that repeat in a pattern, for example, 0.666… or 0.142857142857…

    NUMBER SYSTEMS – Learning Resources

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