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Explain why the sum of a rational number and an irrational number is an irrational number?
Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)
Is 0.05 a rational or irrational number?
It is a rational number.
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.
Is a rational number times a irrational number?
Can be irrational or rational.1 [rational] * sqrt(2) [irrational] = sqrt(2) [irrational]0 [rational] * sqrt(2) [irrational] = 0 [rational]
Which number can be added to a rational number to explain that the sum of rational number and an irrational number is irrational?
Any, and every, irrational number will do.
Explain why the sum of a rational number and an irrational number is an irrational number?
Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)
Is -6.743743 rational or irrational number explain?
It is a rational number because it is a terminating decimal number which can also be expressed as a fraction
Is the area of one triangle a rational number or an irrational number Explain.?
The area of a triangle can be a rational number or an irrational number depending on its dimensions.
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?
34.5 is RATIONAL. Irrational numbers are those were the decimals go to infinity AND there is no regular order in the decimal numbers. Definitively an Irrational Number CAnnot BE CONVERTED TO A quotient/ratio/frACTION pi = 3.141592.... is the most well known irrational number. So 34.5 is rational 34.55555..... is rational (gOES TO INFINITY ; numbers in regukar order). 34.565656.... is Rational (Goes to infinity ; numbers in regulkar order). et seq., The dots after the number mean it continues to infinity . However, 34.25865414..... is Irrational . Because there is no regular order in the decimal digits.
Is the square root of 133 irrational or rational explain?
It is irrational. 133 = 7*17 and so is not the square of any rational number. Therefore its square root cannot be rational.
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.
