Best Answer

A real number is an irrational number if it cannot be expressed as a fraction a/b, where a and b are integers. Most real numbers are irrational. The most well known Irrational Numbers are π and √2. The inverse condition are called the rational numbers.

Q: When can you say that a given real number is irrational?

Write your answer...

Submit

Still have questions?

Continue Learning about Algebra

It is irrational.

I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.

NO. The word irrational means "cannot be expressed as a ratio". A fraction IS a ratio. For instance: in the ratio 1:3 , the total number of shares is 4(=1+3). The share 1 is 1/4 of the total. Since a fraction is a ratio, it is WRONG to say it is irrational, which would mean it is not a fraction (or ratio). However, it is also good to take note that even an irrational number is a real number.

Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...

from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.

Related questions

The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.

Yes. Together, they make up the entire set of real numbers. That is to say, any real number is either rational or irrational.

It is irrational.

A whole number is definitely a real number! For example say you have the number 7. 7 is a real number, because it doesn't have any decimals or fractions! Hope that helps! A whole number is a real number. A real number can be a fraction, a negative, a positive number, rational, or an irrational number. A whole number is a positive number or zero.

I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.

NO it is not irrational, that is to say it IS rational. If you can write a number as ratio of integers, it is rational. -11.7 can certainly be written as a ratio of integers.

NO. The word irrational means "cannot be expressed as a ratio". A fraction IS a ratio. For instance: in the ratio 1:3 , the total number of shares is 4(=1+3). The share 1 is 1/4 of the total. Since a fraction is a ratio, it is WRONG to say it is irrational, which would mean it is not a fraction (or ratio). However, it is also good to take note that even an irrational number is a real number.

The simplest example (of infinitely many) is probably the squareroot of two multiplied by itself equals two. Take any rational number, say 4.177 and divide it with any irrational number, say the square root of 13, and you will get a new irrational number. The product of your two irrational numbers now make a rational number.

A mathematical approach:Yes they are. Irrational numbers are very real, for example - the square root of two - which is irrational (but can be plotted in a number line without difficulty with a compass and straight edge). All numbers you can think of (even if you cant white them out) are real numbers.They are real, but they can't be expressed as fractions.A philosophical approach:According to ME, there should be a limit. If there is a number which is not ending, we can't say that it is a number because it has not ended yet, its not a complete number. That's why, any number which is not ending is not a number, so irrational numbers and some rational numbers are not numbers and we can't plot them on real line, no matter how much depth we are into it. If there is a number 1.0000... (100 million 0's) ...1, we can plot it by dividing real line into required many parts but we cant plot a number like 1.1111....1111....(up to, we don't know), actually that's not a number yet.Maths should be changed.

False.False.

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.

Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...