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What else can I help you with?
Is it true that sum of a rational number and irrational number is irrational?
Yes
Can the product of any two irrational numbers be a rational number?
Yes. For example, if you multiply the square root of 2 (an irrational number) by itself, the answer is 2 (a rational number). The golden ratio (Phi, approx. 1.618) multiplied by (1/Phi) (both irrational numbers) equals 1 (rational). However, this is not necessarily true for all irrational numbers.
Why an irrational number plus an irrational number equal a rational?
Well, darling, when you add two irrational numbers together, they can sometimes magically cancel each other out in such a way that the sum ends up being a rational number. It's like mixing oil and water and somehow getting a delicious vinaigrette. Math can be a wild ride, honey.
Give x-y is rational number prove that 2x 3y is irrational number?
This can't be proved because it is not necessarily true. If x is 2 and y is 1 then x-y is 1, which is rational. The product of 2x and 3y is 12, which is also rational. Sadly, you can't disprove it either; for certain values of x,y it is true as posited.
Is The product of two rational numbers always a rational number?
Yes, that's true.
What product is true about the irrational and rational numbers?
The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.
Is it always sometimes or never true that the product of a non zero rational number and an irrational number is irrational?
It is always true.
Is the sum of a rational number and an irrational number is irrational true or false?
It is true.
Is it true that sum of a rational number and irrational number is irrational?
Yes
Can the product of any two irrational numbers be a rational number?
Yes. For example, if you multiply the square root of 2 (an irrational number) by itself, the answer is 2 (a rational number). The golden ratio (Phi, approx. 1.618) multiplied by (1/Phi) (both irrational numbers) equals 1 (rational). However, this is not necessarily true for all irrational numbers.
A number is either a rational or an irrational but not both True or False?
True.
Are there more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
Are more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.
What number will produce a rational number when multiplied by 0.5?
Any and every rational number.
Negative sign affects whether or not a number is a rational number?
Only if the negative sign is associated with an even root. In that case, the number is neither rational nor irrational, but is imaginary.
Is it true that if you add two irrational numbers you will always get a rational number?
yes
Why does the sum of rational number and irrational numbers are always irrational?
Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.
