0
No.
The easiest counter-example to show that the product of two Irrational Numbers can be a rational number is that the product of √2 and √2 is 2.
Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.
Still curious? Ask our experts.
Chat with our AI personalities
Taiga
Fran
ProfessorAdd your answer:
Earn +20 pts
Does an irrational number times an irrational number equal an irrational number?
Not always. For example sqrt(2) and 1/sqrt(2) are both irrational, but their product is the rational number 1.
Is the product of two irrational numbers always an irrational number?
No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.
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 real number is always a rational number?
They are not. Sometimes they are irrational. Irrational numbers cannot be expressed as a fraction.
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.
