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Sum/Product - Rationals or Irrationals bsci-ch.org

Topical summary | Algebra 1 synopsis | MathBits" Teacher resources terms of Use contact Person: Donna Roberts


"The amount of 2 rational numbers is rational."

By definition, a reasonable number can be expressed together a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rationals is the very same as including two together fractions, which will result in another fraction of this same kind since integers are closed under addition and multiplication. Thus, adding two rational numbers produces one more rational number.

You are watching: The sum of two irrational numbers is always irrational

Proof:

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"The product of two rational numbers is rational."

Again, by definition, a reasonable number deserve to be expressed together a portion with integer worths in the numerator and also denominator (denominator no zero). So, multiplying two rationals is the very same as multiplying 2 such fractions, i beg your pardon will an outcome in another portion of this same type since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.

Proof:

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look out! This next component gets tricky!!

"The amount of 2 irrational number is periodically irrational."

The amount of 2 irrational numbers, in part cases, will be irrational. However, if the irrational components of the numbers have actually a zero amount (cancel each other out), the sum will be rational.

See more: Design A Synthesis Of 2-Butanone From Ethyne., Butan−2−One From Ethyne

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"The product of two irrational numbers is periodically irrational."

The product of two irrational numbers, in some cases, will be irrational. However, it is possible that some irrational numbers may multiply to kind a reasonable product.

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Topical rundown | Algebra 1 summary | bsci-ch.org | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts