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Can you subract an rational and irrational number and get an irrational number?
Yes. In fact, a rational plus or minus an irrational will always be irrational.
Why does the sum of rational number and irrational numbers are always 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.
Is 4.5 irrational?
4.5 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
How is the sum of a rational and irrational number irrational?
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.
Is -0.45 an irrational number?
No - expressed as a fraction in its simplest form, -0.45 is equal to -9/20 or minus nine twentieths.
What is an irrational number minus a rational number?
It is an irrational number.
Can you subract an rational and irrational number and get an irrational number?
Yes. In fact, a rational plus or minus an irrational will always be irrational.
Is a rational number minus a rational number a rational number?
Yes because a rational number can be expressed as a fraction whereas irrational numbers can't be expressed as fractions.
Is - square root 17 irrational rational irrational whole irrational rational?
17 is a prime number with no factors other than itself and 1 therefore minus square root of 17 is an irrational number.
Is π minus e rational or irrational?
Irrational.
Is minus point 4744 rational or irrational?
Any number with a defined end-point, such as -0.4744, is rational.
What irrational number can be added to pi to get a sum that 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
Is the square root of 36 - 25 rational or irrational?
If you mean 36 minus 25 then the square root of 11 is an irrational number
Why does the sum of rational number and irrational numbers are always 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.
Can you add two irrational numbers that are not conjugates of one another ie a plus b and a minus b to get a rational 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.
Is 4.5 irrational?
4.5 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
How is the sum of a rational and irrational number irrational?
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.
