Why Adding a Rational Number and Irrational Number Always Results in an Irrational Number: Explanation and Examples.

sum of rational number and irrational number is

When it comes to adding a rational number and an irrational number, the result is always an irrational number

When it comes to adding a rational number and an irrational number, the result is always an irrational number.

To understand why, let’s start by defining what a rational number is. A rational number is a number that can be expressed as the quotient of two integers, where the denominator is not zero. In other words, it can be written as a fraction.

On the other hand, an irrational number cannot be expressed as a simple fraction or ratio of two integers. Examples of irrational numbers include √2, π, and e.

Now, when we add a rational number and an irrational number, let’s say “a” (rational) and “b” (irrational), we can express the sum as:

a + b

Since “a” is a rational number, it can be written as a fraction:

a = c/d

Where “c” and “d” are integers, and “d” is not zero.

Now let’s substitute this into the sum:

c/d + b

To simplify this expression, we need to obtain a common denominator. However, no matter what denominator we choose, “b” will always remain an irrational number.

Therefore, the sum of a rational number and an irrational number remains an irrational number.

More Answers:

Simplifying the Expression 1 + cot^2(x): A Trigonometric Approach
Understanding the Relationship between Sin(x) and Sin(-x): Exploring the Symmetry and Sign Change of Sine Function
The Rationality of Addition and Multiplication: The Invariable Rationality of the Sum and Product of Two Rational Numbers

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