Question

Prove that 2 + √ 5 is an irrational number

Answer 1

Let if possible suppose ,
2 + Root5 is a rational number
=> (2 + Root5) - 2 is a rational number ( Since , Rational - Rational = Rational )
=> 2 + Root5 - 2 is a rational number
=> Root5 is a rational number
This contradicts the fact that Root5 is an irrational number..Hence our assumption was wrong.
Thus 2 + Root5 is an irrarional number.

Answer 2

suppose 2+root5 is an rational no.
2+root5=p/q pand q are co prime no.
2-p/q= -root5
in l.h.s 2-p/q is an rational no. but in r.h.s -root5 is an irrational no. it is not possible.
so, our supposation is wrong.
2+root5 is an irratinal no.
plz plz plz mark me as a brainlist