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Question

Prove that 3+25 is irrational.

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Solution

Let us assume 3+25 + is rational.

So we can write this number as
3+25=ab ---- (1)

Here a and b are two co-prime number and b is not equal to zero.
Simplify the equation (1) subtract 3 both sides, we get
25=ab3

25=a3bb

Now divide by 2 we get
5=a3b2b

Here a and b are integer so a3b2b is a rational number, so 5 should be a rational number.

But 5 is a irrational number, so it is contradict.

Therefore, 3+25 is irrational number.

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