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Question

Question 2
Prove that 3+25 is irrational.

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Solution

Let's assume that 3+25 is a rational number.
So we can write this number as,
3+25=ab
Here a and b are two co prime integers and b is not equal to 0.
Subtract 3 from both sides, we get,
25=ab3
25=(a3b)b
Now divide by 2; we get,
5=(a3b)b
Since a and b are integers, (a3b)2b is a rational number, then 5 is also a rational number as (a3b)2b is equal to 5 .
But, we know that 5 is an irrational number, so it contradicts our assumption.
Hence, 3+25 is an irrational number.


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