Maths Help?

Question

Is the sum or product of two irrational numbers always irrational?

im not look for a yes or no answer for the 10 points

Answer 1

No

√2 is a irrational number

Multiplying two irrational numbers

(√2)(√2) =

√4 =

2 . . .is a real number

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Answer 2

Nope ... here's a counterexample for a product:

(√3) (√3) = √9 = 3

Also, take a look at the link I included here ... it provides a proof for the sum of a rational and irration number. Your case is similar and it might be helpful.

(If it doesn't come out correctly then go to the website directly using the link below)

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The sum, difference, product and quotient of two non-zero real numbers, from which one is rational and the other irrational, is irrational.

Proof. Let be a rational and irrational number. Here we prove only that is irrational -- the other cases are similar. If were a rational number , then also would be rational as a product of two rationals. This contradiction shows that is irrational.

Note. In the result, the words real, rational and irrational may be replaced resp. by the words complex, algebraic and transcendental or resp. by the words complex, real and imaginary (the last term here meaning, as commonly in Continental Europe, a complex number having non-zero imaginary part).

Answer 3

For example, irra x times irra x gives you answer x.
but, irrational x plus irrational x gives you answer 2irra x

Therefore, the sum gives you irrational answer.

Answer 4

NO sqrt(2) is irrational but sqrt(2)*sqrt(2) is 2 which is not irrational

Answer 5

I'm pretty sure it's the sum