Question

2. Prove that 3+2√5 is irrational.​

Answer 1

Answer:

To prove : 3+2√5 is a irrational no

Step-by-step explanation:

let us assume that 3+√5 is a rational no

so this no. will be written as in the form of a/b

3+2√5 = a/b

2√5 = a/b - 3

2√5 = a - 3b /b

√5 = a - 3b / b × 2b

now LHS is an irrational no

and

RHS is a rational no

hence our assumption is wrong so

therefore hence proved

Answer 2

Suppose 3+2√5 is rational.

Then, it can be written in the form a/b

i.e. 3+2√5=a/b

or, 2√5=a/b - 3

or, 2√5= (a-3b)/b

Now, √5 = 1/2 X (a-3b) /b

→ √5= (a-3b)/2b

In LHS we have an irrational number and in RHS we have rational number.

Since, irrational number cant be equal to a rational number so it is a contradiction, our supposition is wrong and hence, 3+ 2√5 is an irrational number.