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Number systems — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSNumber systems1 Mark
Question
Which of the following is a true statment?
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Answer

  1. Every real number is either rational or irrational.
    Solution:
    Consider, $\big(2+\sqrt{3}\big)$ and $\big(2-\sqrt{3}\big)$ which are two irrational numbers.
    $\big(2+\sqrt{3}\big)+\big(2-\sqrt{3}\big)=4,$ which is a rational number.
    Consider, $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$ which are two irrational numbers.
    $\sqrt{3}\times\frac{1}{\sqrt{3}}=1,$ which is a rational number.
    Every real number can either be a rational number or an irrational number.
    Hence, the correct opion is (d).

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