math question

[EnsignYoshi]

I'm hoping someone can answer these questions for me or direct me to websites where I can find the answers. Thx in advance

1) if you multiply an irrational number with an irrational number, is it possible you'll get a rational number or will it always be an irrational number?

2) if you multiply an irrational number with a rational number. Will the outcome be rational or irrational?

3) if you add an irrational number to an irrational number. Is the answer rational or irrational. And the same question about adding a rational number to an irrational number.

damn, those questions even got me confused

 

[Smiley]

I'm not going to give you actual answers, but if you use fractions to help you visualize the concepts, the problems are pretty simple. Use variations on 1/3 as your irrational numbers and variations on 1/2 and 3 as your rational numbers.

 

[Lindley]

1) if you multiply an irrational number with an irrational number, is it possible you'll get a rational number or will it always be an irrational number?

Turn the question around---is it possible to divide a rational by an irrational and get an irrational?

Most of these questions become more obvious when you look at them backwards.

 

[Yassim]

The first one is obvious (hint - wasn't root 2 the first irrational number ever used mathematically?)

The third one, I can quickly add two irrational numbers to make zero... and I guess I just figured out how to get any rational number, since pi +1 is irrational...

Without thinking *too* hard, I'm gonna say the second one is always irrational. Because it just seems that way.

 

[Lindley]

To add to what I said before....

2) if you multiply an irrational number with a rational number. Will the outcome be rational or irrational?

If you divide a rational by another rational, is it possible for the result to be irrational?

 

[RobertVA]

I'm hoping someone can answer these questions for me or direct me to websites where I can find the answers. Thx in advance

1) if you multiply an irrational number with an irrational number, is it possible you'll get a rational number or will it always be an irrational number?

2) if you multiply an irrational number with a rational number. Will the outcome be rational or irrational?

3) if you add an irrational number to an irrational number. Is the answer rational or irrational. And the same question about adding a rational number to an irrational number.

damn, those questions even got me confused

1. Since there are irrationals that are roots of rational numbers the results could be rational OR irrational (things like multiples of pi).

2. I'm thinking irrational. One is rational and the identity for multiplication (x multiplied by one is always x), thus an irrational multiplied by one would still be irrational. I'm thinking other rationals, except zero, would result in irrational products too.

3 I'm thinking irrational here too, except where you add an irrational and it's opposite (like pi plus the opposite of pi).

I'm not going to give you actual answers, but if you use fractions to help you visualize the concepts, the problems are pretty simple. Use variations on 1/3 as your irrational numbers and variations on 1/2 and 3 as your rational numbers.

But fractions with 3 in the denominator are rational. The "rational" comes from "ratio" as in "1/3", "4/7", and "4 2/3" (14/3).

To add to what I said before....

2) if you multiply an irrational number with a rational number. Will the outcome be rational or irrational?

If you divide a rational by another rational, is it possible for the result to be irrational?

That's pretty much what defines a rational number. Irrational numbers like pi and some roots (like the square roots of two and three) can't be accurately represented by a rational divided by another rational. This doesn't prevent some rationals (like 1/3 and 1/7) from being repeating sequences when converted to decimal. Repeating sequences are the result when neither two or five are factors of the denominator (when the fraction is simplified).

 

[Smiley]

Yes, I'll admit I was wrong. I forgot that nonrandom repeating numbers are rational when I posted my reply. Square roots are more the key to these questions.