No.
The difference can be rational or irrational.5 + sqrt(3) and 2 + sqrt(3) are both irrational numbers but their difference is[5 + sqrt(3)] - [2 + sqrt(3)] = 3, which is rational.
No, 3 is a rational number. Pi and the square root of 2 are irrational numbers.
There are an infinite number of rational numbers.Rational numbers are any number that can be expressed as a ration between 2 other numbers. 2 for example is a ratio of 2/1, 10000 = 10000/1, a half or 0.5 = 1/2 a third or 0.3333333333333reaccuring = 1/3 etc. Irrational numbers are those numbers than cannot be expressed no matter how hard we try to by dividing 2 numbers. Good examples of irrational numbers is square root of 2 (gives us 2 irrational numbers) and the ratio of a circles circumference to its diameter otherwise better known as pi (3.14159265etc,etc,etc). It is from this that we get the word irrational meaning beyond common sense.
The square root of 2 and the square root of 3 both qualify. Both of these are irrational and both are greater than 1 but less than 2. There are, of course, uncountably infinite different irrational numbers in the range between 1 and 2 and countably infinite rational numbers.
here are rational numbers--numbers that you can express as a fraction irrational numbers--numbers you cannot express as a fraction integers--whole numbers and their opposites(negatives) whole numbers--0, 1, 2, 3,... natural or counting numbers--1, 2, 3,....
No. Two irrational numbers can be added to be rational. For example, 1/3 + 2/3 = 3/3. 1/3 and 2/3 are both irrational, but 3/3 = 1, which is rational.
sqrt(2), sqrt(3)
Not necessarily. 3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.
If it is integers, you have -2, -1, 0, 1, 2 and 3. If rational numbers or irrational numbers or real numbers, there are an infinity of them between -3 and 4.
Four examples of irrational numbers are 21/2, 31/2, 51/2 & 71/3
No. The easiest counter-example to show that the product of two irrational numbers can be a rational number is that the product of √2 and √2 is 2. Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.
The difference can be rational or irrational.5 + sqrt(3) and 2 + sqrt(3) are both irrational numbers but their difference is[5 + sqrt(3)] - [2 + sqrt(3)] = 3, which is rational.
The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.
No, 3 is a rational number. Pi and the square root of 2 are irrational numbers.
sqrt(2)*sqrt(3) is an irrational product.
Some are and some aren't. 62 is real and rational. 1/3 is real and rational. sqrt(2) is real and irrational. (pi) is real and irrational.
There are an infinite number of rational numbers.Rational numbers are any number that can be expressed as a ration between 2 other numbers. 2 for example is a ratio of 2/1, 10000 = 10000/1, a half or 0.5 = 1/2 a third or 0.3333333333333reaccuring = 1/3 etc. Irrational numbers are those numbers than cannot be expressed no matter how hard we try to by dividing 2 numbers. Good examples of irrational numbers is square root of 2 (gives us 2 irrational numbers) and the ratio of a circles circumference to its diameter otherwise better known as pi (3.14159265etc,etc,etc). It is from this that we get the word irrational meaning beyond common sense.