Prove the following statement: if x is irrational and y is irrational then x+y is irrational

Prove the following statement: if x is irrational and y is irrational then x+y is irrational

Analyzing categorical data
asked 2021-02-12
Prove the following statement: if x is irrational and y is irrational then x+y is irrational

Answers (1)

If x and yy are both irrational numbers then x+y need not to be irrational number. As a example, take \(\displaystyle{x}=−\sqrt{{{2}}}{\quad\text{and}\quad}{y}={1}+\sqrt{{{2}}},{t}{h}{e}{n}{x}+{y}=−\sqrt{{{2}}}+{\left({1}+\sqrt{{{2}}}\right)}={1},\)
which is rational. But if xx and yy bothrational, say
where a,b,ca,b,c and dd are integers with b,db,d not equal to 0.0. Now
Therefore, x+y is rational since ad+bc,bd are integers and bd not equal to 0.0.

Relevant Questions

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