Question

Show that 5+√2 is an irrational number

Answer 1

5+√2 is an irrational no. because here √2 is irrational no. as the value of √2 is 1.414......
So whole 5+√2 is irrational no.


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Answer 2

Show that 5 +√2 is an irrational number?

Show that 5 +√2 is an irrational number?


So basically the text book has been telling me that the way to do these types of problems is to do these by proof-by-contradiction. I think the proof goes like this:

Assume that 5+√2 is a rational number. Thus, 5+√2 - 5 implies that √2 is a rational number because the difference of two rational numbers is a rational number. We know this is not true, resulting in our original assumption to not be true also. In other words, 5 +√2 is an irrational number

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