The Rational and Irrational Number Addition: Understanding when the result is Rational or Irrational

sum of rational number and irrational number is

The sum of a rational number and an irrational number can be either rational or irrational, depending on the specific numbers being added

The sum of a rational number and an irrational number can be either rational or irrational, depending on the specific numbers being added.

Let’s consider a specific example: the rational number 2/3 and the irrational number √2.

If we add these two numbers together, we get:

2/3 + √2 =

To simplify this expression, we need to convert the rational number 2/3 into an expression involving a common denominator. In this case, we could multiply the numerator and denominator of 2/3 by √2:

2/3 + √2 = (2/3) * (√2/√2) + √2 = (2√2)/(3√2) + √2

Next, we can combine the terms with a common denominator:

= (2√2)/(3√2) + √2 = (2√2 + 3√2)/(3√2) = 5√2/(3√2)

Now, since we have the same square root term in the numerator and the denominator, we can cancel them out:

= 5√2/(3√2) = 5/3

In this case, the sum of the rational number 2/3 and the irrational number √2 is a rational number, 5/3.

However, it’s important to note that this specific example does not represent all possible combinations of rational and irrational numbers. The sum of a rational and an irrational number can also result in an irrational number. The outcome will depend on the specific numbers involved in the addition.

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