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Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
Is the product of three rational numbers rational or irrational?
A rational number in essence is any number that can be expressed as a fraction of integers (i.e. repeating decimal). Taking the product of any number of rational numbers will always yield another rational number.
If x is rational and y is rational then xy is rational?
Yes, the product of two rational numbers is always a rational number.
What The product of two rational numbers?
It is a rational number.
What is always true about the product of 2 mixed numbers?
In any case, being the product of two rational numbers, it will also be rational. It can either be another mixed number, or it may happen to be an integer.
