0
Prove that if a and b are rational numbers then a multiplied by b is a rational number?
If a is rational then there exist integers p and q such that a = p/q where q>0.
Similarly, b = r/s for some integers r and s (s>0)
Then a*b = p/q * r/s = (p*r)/(q*s)
Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0
Thus a*b can be expressed as x/y where
p and r are integers implies that x = p*r is an integer
q and s are positive integers implies that y = q*s is a positive integer.
That is, a*b is rational.
What else can I help you with?
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
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.
What fractional form of 9.546 to prove that it is a rational number?
9.546 as an improper fraction in its simplest form is 4773/500 which proves that it is a rational number
How you prove that -if r is rational and x is irrational then prove that r x and rx are rational?
To prove that if (r) is rational and (x) is irrational, then both (rx) and (\frac{r}{x}) are rational, we can use the fact that the product or quotient of a rational and an irrational number is always irrational. Since (r) is rational and (x) is irrational, their product (rx) must be irrational. Similarly, the quotient (\frac{r}{x}) must also be irrational. Therefore, we cannot prove that both (rx) and (\frac{r}{x}) are rational based on the given information.
Prove that the decimal number 4.56 is rational by finding its fractional form?
4.56 = 456/100 = 114/25 or 414/25
Which number can be multiplied to a rational number to explain that the product of two rational numbers is rational?
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Are all rational numbers whole numbers prove your answer?
No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
How can you determine if a number is rational?
If the number can be expressed as a ratio of two integer (the second not zero) then the number is rational. However, it is not always a simple matter to prove that if you cannot find such a representation, then the number is not rational: it is possible that you have not looked hard enough!
How do you prove the set of rational numbers are uncountable?
They are not. They are countably infinite. That is, there is a one-to-one mapping between the set of rational numbers and the set of counting numbers.
Erika knows that when you add two rational numbers you get ar rational number therefor she concludes that the sum of two irrational numbers is irrational prove her wrong?
1+sqrt(2) and 1-sqrt(2) are both irrational but their sum, 2, is rational.
Is there a rational number between any two distinct rational numbers?
Yes. Not only that, but there are an infinite number of rationals between any two distinct rationals - however close. We can prove it like this: Take any three rational numbers, call them A, B and C, where B is larger than A, and C is any rational number greater than 1: D = A + (B - A) / C That gives us another rational number, D, no matter what the values of the original numbers are.
Math help can anyone show you how to do this please Prove or disprove that if a and b are rational number then a to the power of b is rational?
2 and 1/2 are rational numbers, but 2^(1/2) is the square root of 2. It is well known that the square root of 2 is not rational.
Is a rational number divided by an irrational number always irrational?
No. If we let x be irrational, then 0/x = 0 is a counterexample. However, if we consider nonzero rational numbers, then our conjecture is true. We shall prove this by contradiction. Suppose we have nonzero rational numbers x and y, and an irrational number z, such that x/z = y. Since z is not equal to 0, x = yz. Since y is not equal to 0, x/y = z. Since x/y is a quotient of rational numbers, x/y is rational. Therefore, z is rational, contradicting our assumption that z was irrational. QED.
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.
Who was the first person to prove that pi was not a rational number?
Johann Heinrich Lambert
Is 11 squared rational or irrational?
It's the ratio of 121 to 1, so it's rational. I think the square of any rational number is a rational number. In fact, I'm sure of it, because I know how I could prove it.
