Question

plz answer this question​

Answer 1

${\huge{\green{\underline{\underline{\sf {\mathfrak{Answer}}}}}}}$

${\bf{\orange{\underline{Given:}}}}$

• $To \ prove \ 5+3\sqrt2 \ is irrational$

${\bf{\orange{\underline{Solution:}}}}$

$\sf{\pink{\underline{\bigstar Let:}}}$

$5+3\sqrt2 \ is\ rational$

$\implies 5+3\sqrt2 = \dfrac{p}{q} \ \\ p \ and\ q \ are \ co \ primes \ and \ q \ is \ not 0$

$\implies 5 + 3 \sqrt2 = \dfrac{p}{q}$

$\implies 3\sqrt2 = \dfrac{p}{q} - 5$

$\implies \sqrt2 = \dfrac{p-5q}{3q}$

As the LHS is rational , RHS is irrational , it is comcluded that our assumption is wrong and thus $5+3\sqrt2$ is irrational.