Rationalizing the Expression: 1/√5 + √3
In this article, we will explore the techniques used to simplify the expression 1/√5 + √3. This expression involves a combination of a rational expression and a square root, making it an interesting case study in algebra.
What is Rationalization?
Rationalization is a process in algebra where we eliminate radicals (square roots, cube roots, etc.) from the denominator of an expression. The goal is to have a simplified expression without radicals in the denominator.
Simplifying the Expression
Let's start by analyzing the given expression:
1/√5 + √3
To simplify this expression, we need to rationalize the denominator of the first term, 1/√5.
Rationalizing the Denominator
To rationalize the denominator, we will multiply the numerator and the denominator of the first term by √5. This will eliminate the radical from the denominator.
(1 × √5) / (√5 × √5) + √3
Simplifying the expression, we get:
√5 / 5 + √3
Combining Like Terms
Since we have two separate terms, we cannot combine them further. The final simplified expression is:
√5 / 5 + √3
Conclusion
In conclusion, we have successfully rationalized the expression 1/√5 + √3, eliminating the radical from the denominator. The simplified expression is √5 / 5 + √3. This process demonstrates the importance of rationalization in simplifying algebraic expressions.
