Question

Prove that 7√3 is an irrational number​

Answer 1

Answer:

7 q - p q is also integer. ∴ is irrational proved. we know sum or difference of two rationals is also rational. ∴ 7-3 is irrational proved.

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Answer 2

$\huge\bf\red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{QUESTION}$

Prove that 7-root 3 is irrational

Let 7-√3 be a rational number

hence,

$\bf{7 - \sqrt{3} = \frac{p}{q} }$

where p and q are integers and q≠0

$\bf{ \implies \: \sqrt{3} = \frac{p}{q} - 7}$

$\bf{ \implies \: \sqrt{3} = \frac{p - 7q}{q} }$

Here ,

$\begin{gathered} \bf{ \frac{p - 7q}{q} is \: rational} \\ \\ \bf{but \: \sqrt{3} is \: irrational} \\ \\ \bf{hence \: the \: contradiction \: we \: } \\ \\ \bf{supposed \: is \: wrong}\end{gathered}$

$\begin{gathered} \huge \mathfrak{hence} \\ \\ \huge \mathfrak{ \sqrt{3} \: is \: irrational}\end{gathered}$