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Q: Can you add two irrational numbers to get an rational number?

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

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)

Yes. sqrt(2), 2*sqrt(2) and -3*sqrt(2).

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.

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.

Related questions

no

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

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.

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.

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

No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.

An irrational number.

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

Rational and Irrational Numbers

yes

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