Irrationality

Number Theory Level 2

Does the product of 2 irrational numbers have to be irrational? If so, give an example. If not, why not?

No Yes Depends

Geoff Liu by Geoff Liu , 18, Australia

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1 solution

Aashish Cheruvu
Oct 1, 2017

sqrt 2 and sqrt 8 are irrational. If we multiply them together we get 4 which is rational.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

But everytime , product of 2 irrational number is not rational. It depends on the question Like : 1. (2+ sqrt3)*(sqrt2), this gives an irrational answer as a product 2. (Sqrt 2) * (sqrt 8), here product is rational . Hence, it depends on the question

Raj Mantri - 3 years, 8 months ago

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He is asking if the product of two irrational numbers must necessarily be irrational. Thus, the answer is no, it must not necessarily be irrational since there are products of irrational numbers that are rational.

Zach Abueg - 3 years, 8 months ago

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