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Do you mean can we subtract one rational number from another rational number and get an irrational number as the difference? I'm not a mathematician, but I suspect strongly the answer is no. Wouldn't this imply that we can sometimes add a rational number to an irrational one, and get a rational number as a sum? That doesn't seem possible.

Ans 2.

It isn't possible. Proof :-

Given two rational numbers, multiply the two denominators.

Express each rational in terms of the common multiple.

Algebraically add the numerators of the new rational numbers.

Put this over the common multiple; there's the result expressed as a ratio.

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Q: Can you subtract two rational numbers and get an irrational number?

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It is an irrational number.

-6.3 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

Rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.

Some irrational numbers can be multiplied by another irrational number to yield a rational number - for example the square root of 2 is irrational but if you multiply it by itself, you get 2 - which is rational. Irrational roots of numbers can yield rational numbers if they are raised to the appropriate power

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-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.

No. Real numbers are divided into two DISJOINT (non-overlapping) sets: rational numbers and irrational numbers. A rational number cannot be irrational, and an irrational number cannot be rational.

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