Best Answer

An irrational number is a real number that cannot be expressed as a ratio of two integers.

Q: What statement explains why is an irrational number?

Write your answer...

Submit

Still have questions?

Continue Learning about Other Math

No. The sum of an irrational number and any other [real] number is irrational.

Close. But to make that statement correct, three letters must be deleted:Every natural number is a[n ir]rational number.

A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.

Related questions

I linked a good resource that explains what you asked below.

The statement is false; in fact, no irrational number can be exactly expressed as a quotient of integers because this property is the definition of rational numbers.

Irrational numbers are real numbers.

An 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. The sum of an irrational number and any other [real] number is irrational.

The sum of a rational and irrational number must be an irrational number.

Close. But to make that statement correct, three letters must be deleted:Every natural number is a[n ir]rational number.

No, 3.56 is not an irrational number. 3.56 is rational.

rational * irrational = irrational.

-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.

A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.