Sum/Product - Rationals or Irrationals rebab.net
"The sum of 2 rational number is rational."
By definition, a rational number can be expressed as a fraction with integer worths in the numerator and denominator (denominator no zero). So, adding two rationals is the same as including two together fractions, which will result in another portion of this same type since integers are closed under addition and multiplication. Thus, including two rational number produces another rational number.
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"The product of 2 rational numbers is rational."
Again, through definition, a rational number deserve to be expressed as a fraction with integer values in the numerator and denominator (denominator no zero). So, multiplying 2 rationals is the same as multiplying 2 such fractions, which will an outcome in another portion of this same form since integers space closed under multiplication. Thus, multiplying 2 rational number produces an additional rational number.
"The sum of two irrational number is periodically irrational."
The amount of two irrational numbers, in part cases, will be irrational. However, if the irrational parts of the numbers have actually a zero amount (cancel each various other out), the amount will be rational.
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"The product of two irrational numbers is sometimes irrational."
The product of two irrational numbers, in some cases, will certainly be irrational. However, that is possible that some irrational numbers may multiply to form a rational product.
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