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Why the product of nonzero rational number and an irrational number is an irrational?
Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;write ax = b where b is rational.Then x = b/a, and x would be rational, contradiction.
Why is the sum of an rational number and irrational number an irrational number?
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
Is the number 0.3333 is irrational?
This is a rational number because it terminates at the 4th 3. If it was 0.3 recurring then it would be irrational.
Can an irrational number become a rational number?
How would you do that ?? You'd have to change the value of the number. As long as the irrational number keeps its original value, it's an irrational number.
Is 2.8333333 a rational number or irrational number?
A rational number is any number that does not have an infinite number of digits. So, as you wrote it, 2.8333333 is a rational number. However, if you meant the 3s to go on forever (as in the number 2.8 + 1/30), that would be an irrational number.
How do you Represent irrational number on number line?
The same as you would a rational number. Its distance from zero will represent the number, whether it is rational or irrational.
How can you compare rational and irrational numbers?
Rational number can be divided into more that the number 2. Irrational number are numbers that can only be divided evenly with the number 2.
Is a number either rational or irrational but not both?
Yes. A number can be either rational or irrational, but never both; otherwise there would be an inherent contradiction.
Can you add two irrational numbers and get a rational number?
Yes - if I had an irrational number x, and I added that to the number (7-x), I would end up with 7.If the number is irrational, it can be subtracted from a rational/integer to make another irrational.
Why the product of nonzero rational number and an irrational number is an irrational?
Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;write ax = b where b is rational.Then x = b/a, and x would be rational, contradiction.
Is 0.83 an irrational number?
I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.
Why is the sum of an rational number and irrational number an irrational number?
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
Is the number 0.3333 is irrational?
This is a rational number because it terminates at the 4th 3. If it was 0.3 recurring then it would be irrational.
Can an irrational number become a rational number?
How would you do that ?? You'd have to change the value of the number. As long as the irrational number keeps its original value, it's an irrational number.
Is the square root of -144 rational or irrational?
It is irrational, because it is not a perfect square. For example, if you have a number that is perfect like the square root of 100, it would be 10, which is a rational number. An irrational number like 16.4 which would be a not so accurate result like 6.447583839, those are irrational numbers. Hope this helps!
Is the square root of 10 over 2 rational or irrational?
The result would be an irrational number
Is 81 a rational or irrational number?
81 as well as all whole numbers are rational numbers. Any number that can be written as a fraction is a rational number. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. An example of an irrational number would be pi: π = 3.141592…
