0
Yes. The proof is easy. Let x be the irrational number and assume there exists some rational number r = a/b where a and b are integers (that's what it means to be rational).
Now suppose x/r is a rational number. Then x/r = (b/a)x = c/d where c and d are some other integers.
Since (b/a)x=c/d, then
x = bd/ac
which means that x itself is rational, but we assumed it was irrational.
The contradiction proves that the assertion is wrong. An irrational divided by a rational must be irrational.
Still curious? Ask our experts.
Chat with our AI personalities
Lao
Blake
JudyAdd your answer:
Earn +20 pts
Is an irrational number divided by an irrational number always a rational?
No. sqrt(2)/pi is not rational.
When an irrational number is divided by a rational number is the quotient rational or irrational?
Irrational.
Is the product of a rational number and irrational number always rational?
No.A rational times an irrational is never rational. It is always irrational.
Can An irrational number divided by an irrational number equals a rational number?
Yes. Any irrational number can be divided by itself to produce 1, which is a rational number.
Is the sum of a rational and irrational number rational or irrational?
It is always irrational.
Is an irrational number divided by an irrational number always a rational?
No. sqrt(2)/pi is not rational.
When an irrational number is divided by a rational number is the quotient rational or irrational?
Irrational.
What happens when a rational number is divided by an irrational number?
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.
Is the product of a rational number and irrational number always rational?
No.A rational times an irrational is never rational. It is always irrational.
Can An irrational number divided by an irrational number equals a rational number?
Yes. Any irrational number can be divided by itself to produce 1, which is a rational number.
Is the sum of a rational and irrational number rational or irrational?
It is always irrational.
Is the product of a nonzero rational number and an irrational number rational or irrational?
It is always irrational.
When you multiply an irrational number by a rational number will the answer always be irrational rational or both?
It will be irrational.
Can you multiply an irrational number by a rational number and the answer is rational?
The product of an irrational number and a rational number, both nonzero, is always irrational
What is the product of rational and irrational number?
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
Is the product of a rational number and an irrational number rational or irrational?
Such a product is always irrational - unless the rational number happens to be zero.
Can you add irrational number and a rational to get a rational number?
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
