Question

prove that 3+2√5 is irrational​

Answer 1

suppose 3+2✓5 is the rational number and can be written in form of p/q

3+2✓5=p/q

2✓5=p/q-3

✓5=1/2(p/q-3)

we know that ✓5is the rational number

which is the contradiction with the fact that 3+2✓5is an irrational number

Answer 2

Answer:

by the method of contradiction .

let us assume that 3+2√5 is a rational number .

so ,

3+2√5 = a ÷ b

√5       = a÷2b - 3

so ,

here a÷ 2b- 3 is rational number

but ,

it is said that √ 5 is irrational

this contradiction has arisen due to our incorrect assumption .

this contradicts the fact that ,

3+2√5 is an irrational number