Question

prove that 7+√3 is irrational
number​

Answer 1

Explanation:

UESTION

Prove that 7-root 3 is irrational

Let 7-√3 be a rational number

hence

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

where p and q are integers and q≠0

\bf{ \implies \: \sqrt{3} = \frac{p}{q} - 7}⟹3=qp−7

\bf{ \implies \: \sqrt{3} = \frac{p - 7q}{q} }⟹3=qp−7q

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}qp−7qisrationalbut3isirrationalhencethecontradictionwesupposediswrong

\begin{gathered}\huge \mathfrak{hence} \\ \\ \huge \mathfrak{ \sqrt{3} \: is \: irrational}\end{gathered}hence3isirrational