Question 2
Prove that 3+2√5 is irrational.
Let's assume that 3+2√5 is a rational number.
So we can write this number as,
3+2√5=ab
Here a and b are two co prime integers and b is not equal to 0.
Subtract 3 from both sides, we get,
2√5=ab−3
2√5=(a−3b)b
Now divide by 2; we get,
√5=(a−3b)b
Since a and b are integers, (a−3b)2b is a rational number, then √5 is also a rational number as (a−3b)2b is equal to √5 .
But, we know that √5 is an irrational number, so it contradicts our assumption.
Hence, 3+2√5 is an irrational number.