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Can you add two irrational numbers to get a rational 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.
Does an irrational number multiplied by an irrational number equal an irrational number?
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.
Give the difference between rational and irrational numbers Give examples of each?
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.
Are the square roots of all positive integers irrational If not give an example of the square root of a number that is a rational number?
The square root of any positive square number is always rational as for example the square root of 36 is 6 which is a rational number.
Can you add two irrational numbers to get an irrational number?
Yes.An example:1 + 2^(0.5) is an irrational number,1 -(2^(0.5)) is also a irrational number.(1 + 2^(0.5)) + (1- 2^(0.5)) = 22 is a rational number.Therefore the sum of two irrational numbers can equal a rational number.But this is not the question. Can you add two irrational numbers to get another irrational number. Yes. Almost all additions of two irrational numbers result in another irrational number. For instance pi (3.141...) and e (2.718...) are both irrational, and so is their sum. In some sense you have to work quite hard to make the sum not irrational (i.e. rational) because the two decimal expansions have to conspire together either to cancel out or to give a repeating decimal.Actually, pi+e may or may not be irrational. This hasn't been proved either way. See: http://en.wikipedia.org/wiki/Irrational_number (under "Open Questions")Yes. For example, pi + (-pi) = 0.any number that is a non-terminating decimal is called an irrational number.
Can you add an irrational number and a rational number to give an irrational?
No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.
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.
Does dividing an rational number by an irrational number give you an irrational number?
Yes normally it does
Is negative 2pi a rational number?
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.
Is 0.692 rational or irrational?
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.)
Can you add two irrational numbers to get a rational 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.
Can you give me a whole number that is not a rational number?
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.
Are irrational numbers closed under subtraction?
No, they are not. An irrational number subtracted from itself will give 0, which is rational.
Does an irrational number multiplied by an irrational number equal an irrational number?
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.
Can you please give me an example of an irrational number and a rational 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.
Give the difference between rational and irrational numbers Give examples of each?
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.
Is 2468 rational or irrational?
The number 2468 is a rational number. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. In this case, 2468 can be expressed as the ratio 2468/1, which makes it a rational number.
