sum or product of two irrational numbers is
The sum or product of two irrational numbers can be either rational or irrational
The sum or product of two irrational numbers can be either rational or irrational.
Let’s consider the sum first. Suppose we have two irrational numbers, a and b. When we add them together (a + b), there are two possibilities:
1. If a + b is rational, then the sum of two irrational numbers is rational.
Example: √2 + (-√2) = 0, which is a rational number.
2. If a + b is irrational, then the sum of two irrational numbers is irrational.
Example: √2 + √3 = √2 + √3 (irrational).
Now, let’s consider the product. Suppose we have two irrational numbers, c and d. When we multiply them (c * d), there are also two possibilities:
1. If c * d is rational, then the product of two irrational numbers is rational.
Example: √2 * (√2) = 2, which is a rational number.
2. If c * d is irrational, then the product of two irrational numbers is irrational.
Example: √2 * √3 = √6 (irrational).
Therefore, we conclude that the sum or product of two irrational numbers can be either rational or irrational, depending on the specific values of the irrational numbers involved in the operation.
More Answers:
Why the Sum or Product of Two Rational Numbers is Always a Rational Number: Understanding Rational Number OperationsThe Rational and Irrational Number Addition: Understanding when the result is Rational or Irrational
The Rational and Irrational Numbers: Understanding the Possibilities of Their Multiplication