Question

Prove that 2+3√2 is an irrational number

Answer 1

Let take that 2+3√5 is a rational number.

So we can write this number as

2+3√5 = a/b

Here a and b are two co prime number and b is not equal to 0

Subtract 2 both sides we get

3√5 = a/b *2

3√5 = (a-2b)/b

Now divide by 3 we get

√5 = (a2b)/3b

Here a and b are integer so (a-2b)/3b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact

Hence result is 2+3√5 is a irrational number