Question

show that 3+2root 5is an irrational number​

Answer 1

Answer = let us assume the opposite ,

.i.e,3+2√5 is rational

Hense, 3+2√5 canbe written in the form of a/b

where a and b (b≠0) are co prime (no commen factor othet than 1)

Hense, 3+2√5=a/b

2√5= a/b-3

2√5=a-3b/b

√5 =1/2 X a-3b/b

√5=a-3b/2b

Here=a-3b/2b is a Rational number

but √5 is irrational

sinse rational ≠irrational

this is a contradiction

our assumption is incorrect

Hense 3+2√5 is irrational

Hense proved