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Number systems — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSNumber systems1 Mark
Question
Which of the following is a correct statement?
✓

Answer

  1. Sum of a rational and irrational number is always an irrational number.

    Solution:
  1. Is incorrect, because sum of two irrational numbers is not an irrational number always. It can also be a rational number
    i.e. if we add $2+\sqrt{3}$ and $2-\sqrt{3},$ sum comes out to be $2+\sqrt{\not\text{3}}+2-\sqrt{\not\text{3}}=4,$ which is a rational number.
  1. Is correct, if a rational number is added to an irrational number means to a Non- terminating-repeating number, the sum will also be non-terminating and Non-repeating number, i.e an irrational number.
    Example: a rational number '2' and an irrational no $'\sqrt{3}'$ is added, sum $=2+\sqrt{3}$ which is again a non-terminating and non-repeating number, hence an irrational number always.
  1. Is incorrect, Square of an irrational number is not necessarily a rational number. Again it can be either a rational or irrational.
    i.e $(\sqrt{2})^2=2$ (Rational)
    $(2+\sqrt{3})^2=4+3+2\times2\sqrt{3}=7+4\sqrt{3}$ (irrational)
  1. Is incorrect, Sum of two rational numbers can be an integer and a rational number both.
    i.e $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$ (Rational number)
    Hence, correct option is (b).

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