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Q: Can you add an irrational number and a rational number to give an irrational?

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An irrational number.

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

You can add any irrational number.

Every time. No exceptions.

no

no

Yes. The sum of two irrational numbers can be rational, or irrational.

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.

They add up to 17.02 which is rational number

Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.

Not necessarily. The sum of two irrational numbers can be rational or irrational.

no

no

You wont be able to add a rational number and an irrational number and get a number not in a fraction ( 3 + 22/7) (21/7 + 22/7 = 43/7) So, yes as you see in the example above it made another irrational number.

Yes - if I had an irrational number x, and I added that to the number (7-x), I would end up with 7.If the number is irrational, it can be subtracted from a rational/integer to make another irrational.

Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)

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.

yes

an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.

Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20.

No. The set of rational numbers is closed under addition (and multiplication).

Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.

For two rational numbers select any terminating or repeating decimal number which starts with 2.10 and for irrational numbers you require a non-terminating, non-repeating decimal which also starts with 2.10.

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.

Suppose A = 2 + sqrt(3) and B = 5 - sqrt(3) Then A and B are two irrational numbers but A + B = 2 + sqrt(3) + 5 - sqrt(3) = 7 which is rational.