Question

Prove that 7-√3 is an irrational

Answer 1

HERE IS UR ANSWER FRIEND:-

7-ROOT3 IS AN IRRATIONAL AS IT IS NOT IN THE FORM P BY Q.

HOPE IT HELPED U FRIEND!!✌✌

Answer 2

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

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 ,

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

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