Checking the Rationality of (3 - √2) (3 + √2)
In this article, we will investigate whether the expression (3 - √2) (3 + √2) is rational or not.
Rational Numbers
A rational number is a number that can be expressed as the quotient or fraction of two integers, i.e., p/q where q is non-zero. Examples of rational numbers include 1/2, 3/4, and 22/7.
The Given Expression
The given expression is (3 - √2) (3 + √2). At first glance, it may seem like a complex expression, but let's break it down and analyze it.
Expanding the Expression Let's expand the expression using the distributive property of multiplication over addition:
(3 - √2) (3 + √2) = 3(3 + √2) - √2(3 + √2)
= 9 + 3√2 - 3√2 - 2
= 9 - 2
= 7
The Result
Simplifying the expression, we get 7, which is an integer. Since 7 can be written as 7/1, it is a rational number.
Conclusion
Therefore, we can conclude that the expression (3 - √2) (3 + √2) is indeed rational.
