Rational and Irrational Numbers — MATHEMATICS STD 9 — Question
ICSE BoardEnglish MediumSTD 9MATHEMATICSRational and Irrational Numbers2 Marks
Question
Show that Negative of an irrational number is irrational.
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Answer
Let us assume that $\mathrm{x}$ is an irrational number such that $-\mathrm{x}$ is rational.
So, $-\mathrm{x}=\frac{\mathrm{a}}{\mathrm{b}}$ where $\mathrm{a}, \mathrm{b}$ are integer and $\mathrm{b} \neq 0$
$x=\frac{-a}{b}$
Since, $-\mathrm{a}, \mathrm{b}$ is also integer and $\mathrm{b} \neq 0$.
So $\mathrm{x}$ is a rational number it contradict our assumption.
$\therefore-\mathrm{x}$ is irrational.
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