The connection between rational numbers and irrational numbers? Is the sum, difference, product, division and square of two irrational numbers irrational? Is the sum, difference, product, division and square of rational and irrational numbers irrational? Please explain the reason and give examples. Thank you. If you answer well, it will increase the reward!

The connection between rational numbers and irrational numbers? Is the sum, difference, product, division and square of two irrational numbers irrational? Is the sum, difference, product, division and square of rational and irrational numbers irrational? Please explain the reason and give examples. Thank you. If you answer well, it will increase the reward!

Sum of irrational numbers: can be rational numbers, consider the product of irrational numbers added by opposite numbers: can be rational numbers, multiplication of two identical roots, division of irrational numbers: can be rational numbers, division of two identical roots, square of irrational numbers: can be rational numbers, multiplication of two identical roots, sum of rational numbers and irrational numbers: 1