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Can adding a rational number with an irrational number give you a rational number?

User Pol Lluis
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Well, let’s try √2 - 1/2

So let’s see if √2 - 1/2 = rational number . We can rewrite that as

√2 = rational number + 1/2

But we have the same problem as before. An irrational number can’t be equal to a rational number. So that means √2 - 1/2 is irrational, too.

What if we tried √2 + 2 ?

Well, we can say √2 + 2 = rational number or √2 = rational number − 2 .

That doesn’t work either. √2 + 2 has to be irrational.

So therefore sum of an irrational and a rational number must be irrational.

User Starbax
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