Question

prove that √2+√3 is an irrational no​

Answer 1

Answer:

as we know that

√2 and √3 is irrational number

let , us assume that √2+√3 is rational number

so , we can write it in p/q form

let , a/b = √2+√3

√2+√3 = a/b

√2+√3 is not equal to a/b

because a/b is rational while both root 3 and root 2 is irrational

our assumption is wrong

so , we can say √2+√3 is irratinal

hence , proved

Answer 2

$\huge\bf{\red{\underline{\underline{\mathcal{AnSwer}}}}}$

let (√2+√3 = x) which is a rational no.

:$\implies$ $\sf √2+√3 = x$

:$\implies$ $\sf (√2+√3)² = x²$

:$\implies$ $\sf (√2)²+(√3)²+2.√2.√3 = x²$

:$\implies$ $\sf 2+3+2√6 = x²$

:$\implies$ $\sf 5+√6 = x²$

:$\implies$ $\sf √6 = x²-5$

• this is a contradiction
• because √6 is irrational whereas x²-6 is rational
• hence, our supposition was wrong
• √2+√3 is an irrational no.