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Yes, it will always be irrational.

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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.

Irrational.

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.

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

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

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.

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.

A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.

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