0
Why will the sum of an irrational number and any other number always be irrational?
Wiki User
∙ 9y ago
The proposition is not true.
pi and -pi are both irrational. But their sum, = 0, is rational.
Wiki User
∙ 7y ago
Add your answer:
Earn +20 pts
Is 1 plus the square root of 7 rational or irrational?
The square root of any positive integer can only be a WHOLE NUMBER or IRRATIONAL, so the square root of 7 is irrational.On the other hand, the sum of a rational and an irrational number is always irrational.
Does a rational number times an irrational number equal a rational number?
No. If the rational number is not zero, then such a product is irrational.
Is 5 over pi a rational or irrational number?
If you divide a rational number by an irrational number, or vice versa, you will ALMOST ALWAYS get an irrational result. The sole exception is if you divide zero (which is rational) by any irrational number.
Does pi times any number equal an irrational number?
Since pi is irrational, its product with any other number is also irrational. The only exception is a multiple of its own reciprocal.
What number can you add to any rational number to obtain an irrational number?
You can add any irrational number.
Is the multiplicative inverse of any irrational number always an irrational number?
Yes.
Is the product of a rational number and an irrational number always irrational?
No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.
Is the product of any rational number and an irrational always irrational?
Yes.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
What does a rational number times an irrational number equal?
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
Is 1 plus the square root of 7 rational or irrational?
The square root of any positive integer can only be a WHOLE NUMBER or IRRATIONAL, so the square root of 7 is irrational.On the other hand, the sum of a rational and an irrational number is always irrational.
Does a rational number times an irrational number equal a rational number?
No. If the rational number is not zero, then such a product is irrational.
Is pi over 2 a whole integer rational or irrational number?
If you multiply or divide an irrational number - such as pi - by ANY rational number (except zero), you will ALWAYS get an irrational number.
Is 5 over pi a rational or irrational number?
If you divide a rational number by an irrational number, or vice versa, you will ALMOST ALWAYS get an irrational result. The sole exception is if you divide zero (which is rational) by any irrational number.
Does pi times any number equal an irrational number?
Since pi is irrational, its product with any other number is also irrational. The only exception is a multiple of its own reciprocal.
What number can you add to any rational number to obtain an irrational number?
You can add any irrational number.
Why is the golden ratio an irrational number?
Because like any other irrational number it can't be expressed as a fraction
