Math and Arithmetic

If you divide a rational number by an irrational number, or vice versa, you will ALMOST ALWAYS get an irrational result. The sole exception is if you divide zero (which is rational) by any irrational number.

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

If you multiply a rational and an irrational number, the result will be irrational.

It is irrational - unless the divisor is 0 in which case the division is not defined.

Unless the rational number is zero, the answer is irrational.

-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.

It the combination is multiplication and the rational number is 0, then the result is rational. Otherwise it is irrational.

When the rational number is 0.

Sqrt(2) is irrational. Multiply by sqrt(4.5). Result is 3 which is rational.

Yes, but only if the rational number is non-zero.

If you multiply an irrational number by ANY non-zero rational number, the result will be irrational.

Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.

Multiply it by 0. The result is 0, which is rational.That is the only way that will work with all irrational numbers.

The result would be an irrational number

No, the result is always an irrational number. In more advanced math it is possible to add an infinite amount of rational numbers by way of Taylor Series and get an irrational number. This is how numbers like "Pi" and "e" are derived.

Only if the negative sign is associated with an even root. In that case, the number is neither rational nor irrational, but is imaginary.

You can not add irrational numbers. You can round off irrational numbers and then add them but in the process of rounding off the numbers, you make them rational. Then the sum becomes rational.

If you multiply two irrational numbers, the result can be rational, or irrational.

The answer requires a bit of mathematics, but goes like this:The product of any 2 rational numbers is a rational number.The product of any 2 irrational number is an irrational number.The product of a rational and an irrational number is an irrational number!Therefore simple logic tells us that there are more irrational numbers than rational numbers. There is a way to structure this mathematically, and I believe it is called an "Inductive Proof".Interesting !I'm going to say "No".I reason thusly:-- For every rational number 'N', you can multiply or divide it by 'e', add it to 'e',or subtract it from 'e', and the result is irrational.-- You can multiply or divide it by (pi), add it to (pi), or subtract it from (pi),and the result is irrational.-- You can take its square root, and more times than not, its square root is irrational.There may be others that didn't occur to me just now. But even if there aren't,here are a bunch of irrational numbers that you can make from every rational one.This leads me to believe that there are more irrational numbers than rational ones.-------------------------------------------------------------------------------------------------------There are infinitely many more irrationals than rationals; this was proved by G. Cantor (born 1845, died 1918). His proof is basically:The rational numbers can be listed by assigning to each of the counting numbers (1, 2, 3,...) one of the rational numbers in such a way that every rational number is assigned to at least one counting number;If it is assumed that every irrational number can be assigned to at least one counting numbers (like the rationals), then with such a list it is possible to find an irrational number that is not on the list; so is it not possible as there are more irrationals than there are counting numbers, which has shown to be the same size as the rational numbers, thus showing that there are more irrationals than rationals.

No. 1) The square root of any positive integer that doesn't happen to be a perfect square is IRRATIONAL.2) If you add a rational and an irrational number, the result is irrational.

If you divide an integer by another integer, the result is a rational number by definition.

If you add, subtract or multiply rational numbers, the result will be a rational number. It will also be so if you divide by a non-zero rational number. But division by zero is not defined.

Any addition, subtraction, multiplication, or division of rational numbers gives you a rational result. You can consider 8 over 9 as the division of 8 by 9, so the result is rational.

1/13 = produces an irreducible result 0.0769230769230769...

sqrt(40) or 2*sqrt(10) Evaluating the above will result in a decimal approximation which will be rational, not irrational.

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