Yes normally it does
No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.
No. The number pi is irrational, and if you multiply an irrational number by a non-zero rational number (in this case, -2), you will get another irrational number.As a general guideline, most calculations that involve irrational numbers will again give you an irrational number.
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.
ANY number with a finite number of decimal digits is RATIONAL.(Also, numbers with an infinite number of decimals may be rational - in which case the digits repeat - or irrational.)
Any number that CAN be represented as a ratio of 2 integers is classified as a rational number (other than that you can't use 0 for the denominator) Any number that CANNOT be represented as a ratio of 2 integers is classified as an irrational number You can't have it both ways - either you can or cannot. To paraphrase Yoda "Can or Cannot - there is no both" NOTE: dividing by zero give you infinity which is a concept not a fixed number and thus neither inherently rational nor irrational
You wont be able to add a rational number and an irrational number and get a number not in a fraction ( 3 + 22/7) (21/7 + 22/7 = 43/7) So, yes as you see in the example above it made another irrational number.
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
No, all whole numbers are rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
No, they are not. An irrational number subtracted from itself will give 0, which is rational.
The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.
An irrational number cannot be written as a fraction or to an exact decimal such as the symbol for pi or the square root of two. A rational number can be written in the form of a fraction or a decimal to an exact value.
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. A rational number can be. 2 is rational. The square root of 2 is irrational.