Give an example of two irrationals whose sum is rational.

Question:

Give an example of two irrationals whose sum is rational.

Solution:

Let the two irrationals be $4-\sqrt{5}$ and $4+\sqrt{5}$.

$(4-\sqrt{5})+(4+\sqrt{5})=8$

​Thus, sum (i.e., 8) is a rational number.

 

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