Every rational number does.
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Any rational number will do.
Yes, it is possible only if an irrational number is multiplied with 0.
Maybe. It depends on the number that you are multiplying. Pi multiplied by (1 / 4pi) = 1/4. A quarter is definitely rational.
Only if the rational number is 0.
Any number will be a rational number when multiplied.0 multiplied by any real number is rational and so it will produce a rational number when multiplied.If x is any non-zero number (rational or not), then since it is non-zero, 1/x is defined and x*(1/x) = 1 which is rational. So any non-zero number will produce a rational number when multiplied.Thus any number will produce a rational number when multiplied.
Every rational number does.
Every rational number does.
Any irrational number multiplied by 0.5 will remain irrational. Any rational number multiplied by 0.5 will remain rational.
Yes, unless the rational number is 0.
Any and every rational number.
Oh, dude, you're talking about squaring a rational number! When you multiply a rational number by itself, you're just squaring it, which means you're multiplying it by itself. It's like saying "Hey, rational number, let's double date with yourself!" So, the product of a rational number multiplied by itself is just that number squared.
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Any already rational number
rational * irrational = irrational.