Q: Can an irrational number minus a rational number equal an irrational number?

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Yes. In fact, a rational plus or minus an irrational will always be irrational.

Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.

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

This can easily be proved by contradiction. Without loss of generality, I will take specific numbers as an example. The proof can easily be extended to any rational + irrational number. Assumption: 1 plus the square root of 2 is rational. (It is a well-known fact that the square root of 2 is irrational. No need to prove it here; you can use any other irrational number will do.) This rational sum can be written as p / q, where "p" and "q" are whole numbers (this is basically the definition of a "rational number"). Then, the square root of 2, which is equal to the sum minus 1, is: p / q - 1 = p / q - q / q = (p - q) / q Since the difference of two whole numbers is a whole number, this makes the square root of 2 rational, which doesn't make sense.

No - expressed as a fraction in its simplest form, -0.45 is equal to -9/20 or minus nine twentieths.

Related questions

It is an irrational number.

Yes. In fact, a rational plus or minus an irrational will always be irrational.

Yes because a rational number can be expressed as a fraction whereas irrational numbers can't be expressed as fractions.

17 is a prime number with no factors other than itself and 1 therefore minus square root of 17 is an irrational number.

Any number with a defined end-point, such as -0.4744, is rational.

Irrational.

Minus pi. Or minus pi plus any rational number. Here is how you can figure this out (call your unknown number "x", and let "r" stand for any rational number):x + pi = r To solve for "x", simply subtract pi from both sides. That gives you: x = r - pi

Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.

If you mean 36 minus 25 then the square root of 11 is an irrational number

You can also have any numbers like (a + c) and (b - c), where "c" is the irrational part, and "a" and "b" are rational.

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

This can easily be proved by contradiction. Without loss of generality, I will take specific numbers as an example. The proof can easily be extended to any rational + irrational number. Assumption: 1 plus the square root of 2 is rational. (It is a well-known fact that the square root of 2 is irrational. No need to prove it here; you can use any other irrational number will do.) This rational sum can be written as p / q, where "p" and "q" are whole numbers (this is basically the definition of a "rational number"). Then, the square root of 2, which is equal to the sum minus 1, is: p / q - 1 = p / q - q / q = (p - q) / q Since the difference of two whole numbers is a whole number, this makes the square root of 2 rational, which doesn't make sense.