No
A rational number is a one that can be written as a fraction i.e a/b. where a and be are integers (whole numbers)
Consider
a/b and c/d. Where a b c and d are integers and as such rational numbers
a/b + c/d = (ad + bd)/cd
ad, bd and cd will all be integers and as such a/b + c/d will always be rational
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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)
Well, darling, when you add two irrational numbers together, they can sometimes magically cancel each other out in such a way that the sum ends up being a rational number. It's like mixing oil and water and somehow getting a delicious vinaigrette. Math can be a wild ride, honey.
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.