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The sum of a rational and an irrational number is always irrational. Here is a brief proof:
Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be an irrational number.
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When an irrational number is divided by a rational number is the quotient rational or irrational?
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 irrational number always rational?
No.A rational times an irrational is never rational. 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.
What is the Next to rational and irrational number?
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
Is 10.01 a rational or irrational number?
10.01 is a rational number
How can you prove that 3 plus 2x⁵ is an irrational number where x⁵ is irrational?
1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
Is 37.5 a rational or irrational number?
Rational
Is 0.05 a rational or irrational number?
It is a rational number.
Is 34.5 rational or irrational?
is 34.54 and irrational or rational. number
Is 4.121314 is a rational number or irrational?
it is a rational number but 4.121314..... is an irrational no
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 an irrational number rational or irrational?
Such a product is always irrational - unless the rational number happens to be zero.
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 there any irrational and rational number?
No number is irrational and rational.
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.
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.
