Question

2. Prove that 3 + 2/5 is irrational.​

Answer 1

Answer:

To prove that 3+2 root 5 is irrational we have to use proof using contradiction method .

Step-by-step explanation:

Let us assume that 3+ 2 root 5 is a rational number such that it can be expressed in the form of p/q where p and q are co prime integers.

3+2root5=p/q

bring 3 to the RHS

2 root5= p/q-3

taking lcm

2root5=(p-3q)/q

Bring 2 to the RHS

root 5= (p-3q)/2q

(p-3q)/2q is a rational number

this implies that root 5 is a rational number

But we know that root5 is irrational

This is a contradition

So, our assumption is wrong

there 3+2root5 is an irrational number.

Answer 2

Answer:

I think the question is 3+2√5

Step-by-step explanation:

Let us assume that, 3+2√5 is rational.

Then 3+2√5= a / b where a and b are coprime and b ≠ 0 .

3+2√5 = a/b

√5 = (a-3)/2b

This contradicts the fact that √5 is irrational.

∴ Our assumption that 3+2√5 is rational is wrong

Hence , 3+2√5 is rational.

HENCE PROVED !!