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Is there any number x such that x² is an irrational number and x's is a rational number?
no x² is the product of 2 rational numbers in this case the same 2 numbers x and x The product of two rational numbers is always rational.
What is meant by additive identity in rational numbers?
The additive identity for rational numbers is 0. It is the only rational number such that, for any rational number x, x + 0 = 0 + x = x
What number equals 79?
1 x 79
Is a rational number is a rational expression?
Any number that can be expressed as a fraction is a rational number otherwise it is an irrational number.
What are 5 properties of addition that apply to rational numbers?
The set of rational number satisfies the following properties with regard to addition: for any three rational numbers x, y and z, · x + y is a rational number (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is a rational number, 0, such that x + 0 = 0 + x = x (existence of additive identity) · There is a rational number, -x, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · x + y = y + x (Abelian or commutative property of addition)
If x is a rational number and y is a rational number than is x plus y rational?
If both numbers are rational then x plus y is a rational number
Show that the sum of rational no with an irrational no is always irrational?
Suppose x is a rational number and y is an irrational number.Let x + y = z, and assume that z is a rational number.The set of rational number is a group.This implies that since x is rational, -x is rational [invertibility].Then, since z and -x are rational, z - x must be rational [closure].But z - x = y which implies that y is rational.That contradicts the fact that y is an irrational number. The contradiction implies that the assumption [that z is rational] is incorrect.Thus, the sum of a rational number x and an irrational number y cannot be rational.
Is there any number x such that x² is an irrational number and x's is a rational number?
no x² is the product of 2 rational numbers in this case the same 2 numbers x and x The product of two rational numbers is always rational.
What is meant by additive identity in rational numbers?
The additive identity for rational numbers is 0. It is the only rational number such that, for any rational number x, x + 0 = 0 + x = x
If you add a rational and irrational number what is the sum?
an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.
Why is the smallest rational number?
There can be no such thing. Given any rational number, x, the number x/2 is also rational and is smaller than x. This process can be continued for ever.
What numbers will produce a rational number when multiplied?
Any number will be a rational number when multiplied.0 multiplied by any real number is rational and so it will produce a rational number when multiplied.If x is any non-zero number (rational or not), then since it is non-zero, 1/x is defined and x*(1/x) = 1 which is rational. So any non-zero number will produce a rational number when multiplied.Thus any number will produce a rational number when multiplied.
What number equals 79?
1 x 79
Is a rational number is a rational expression?
Any number that can be expressed as a fraction is a rational number otherwise it is an irrational number.
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)
What are 5 properties of addition that apply to rational numbers?
The set of rational number satisfies the following properties with regard to addition: for any three rational numbers x, y and z, · x + y is a rational number (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is a rational number, 0, such that x + 0 = 0 + x = x (existence of additive identity) · There is a rational number, -x, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · x + y = y + x (Abelian or commutative property of addition)
Is 0.16 pie a rational number?
(pi) itself is an irrational number. The only multiples of it that can be rational are (pi) x (a rational number/pi) .
