Why Adding a Rational Number and an Irrational Number Always Results in an Irrational Number

sum of rational number and irrational number is

When a rational number and an irrational number are added together, the result is typically an irrational number

When a rational number and an irrational number are added together, the result is typically an irrational number. This is because the sum of a rational number and an irrational number cannot be expressed in the form of a fraction or a whole number.

To understand why this is the case, let’s consider an example:
Let’s say we have the rational number 1/3 and the irrational number √2.

When we add these two numbers together, we get:
1/3 + √2

Since √2 is irrational and cannot be expressed as a fraction or a terminating decimal, the sum cannot be simplified further. Therefore, the result of adding a rational number (1/3) to an irrational number (√2) is an irrational number.

In general, the addition of a rational number and an irrational number will always result in an irrational number. This is because the irrational number introduces a non-repeating, non-terminating decimal component that cannot be expressed as a fraction or a whole number.

More Answers:
The Fundamental Theorem of Algebra | Ensuring Solutions for Polynomial Equations with Complex Coefficients
The Rational or Irrational Results of Adding or Multiplying Irrational Numbers
Understanding Natural Numbers | A Foundation for Mathematical Operations and Concepts

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

Share:

Recent Posts

Don't Miss Out! Sign Up Now!

Sign up now to get started for free!