Presentation of Data in Tabular Form — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsPresentation of Data in Tabular Form2 Marks
Question
Examine whether the following numbers are rational or irrational. $\sqrt{7}-2$
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Answer
Let us assume, to the contrary, that $\sqrt{7}-2$ is rational.
Then, $\sqrt{7}-2=\frac{\text{p}}{\text{q}},$
where $p$ and $q$ are coprime and $\text{q}\neq0.$
$\Rightarrow\sqrt{7}=\frac{\text{p}}{\text{q}}+2$
$\Rightarrow\sqrt{7}=\frac{\text{p}+2\text{q}}{\text{q}}$
Since, $p$ and $q$ are are integers. $\Rightarrow\frac{\text{p}+2\text{q}}{\text{q}}$ is rational.
So, $\sqrt{7}$ is also rational. But this contradicts the fact that $\sqrt{7}$ is irrational.
This contradiction has arisen because of our incorrect assumption that $\sqrt{7}-2$ is rational.
Hence, $\sqrt{7}-2$ is irrational.
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