Rationalizing the Denominator: 1/√7-2
In this article, we will discuss how to rationalize the denominator of the expression 1/√7-2.
What is Rationalizing the Denominator?
Rationalizing the denominator is a process used to remove radicals (square roots, cube roots, etc.) from the denominator of a fraction. This is done to make the fraction more simplified and easier to work with.
The Expression: 1/√7-2
Let's take a closer look at the expression 1/√7-2. This expression has a radical (√7) in the denominator. Our goal is to rationalize the denominator, which means we want to eliminate the radical from the denominator.
Rationalizing the Denominator
To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √7-2 is √7+2.
Multiply both numerator and denominator by √7+2:
(1)(√7+2) / (√7-2)(√7+2)
Simplifying the Expression
Now, let's simplify the expression:
(√7+2) / (√7^2 - 2^2)
Using the difference of squares formula (a^2 - b^2 = (a+b)(a-b)), we can rewrite the denominator:
(√7+2) / (7 - 4)
Simplifying further:
(√7+2) / 3
The Final Answer
The rationalized form of the expression 1/√7-2 is (√7+2) / 3.
In conclusion, we have successfully rationalized the denominator of the expression 1/√7-2, making it easier to work with and simplify further.
