Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Rationalize the Denominator**
Given expression:
\[
\frac{1}{4 - \sqrt{15}}
\]
**Task:** Rationalize the denominator of the given fraction. This involves eliminating the square root from the denominator through multiplication by the conjugate.
**Notes:**
To rationalize a denominator involving a square root, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \(4 - \sqrt{15}\) is \(4 + \sqrt{15}\).
**Example:**
Multiply the fraction by \(\frac{4 + \sqrt{15}}{4 + \sqrt{15}}\):
\[
\frac{1}{4 - \sqrt{15}} \times \frac{4 + \sqrt{15}}{4 + \sqrt{15}}
\]
This approach results in the denominator becoming a difference of squares, allowing for rationalization.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a15759c-8b82-438f-9d6a-36f728df4f17%2F8cd2fb87-0087-40ee-8294-ff279d8d75c8%2Fojyj6pc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Rationalize the Denominator**
Given expression:
\[
\frac{1}{4 - \sqrt{15}}
\]
**Task:** Rationalize the denominator of the given fraction. This involves eliminating the square root from the denominator through multiplication by the conjugate.
**Notes:**
To rationalize a denominator involving a square root, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \(4 - \sqrt{15}\) is \(4 + \sqrt{15}\).
**Example:**
Multiply the fraction by \(\frac{4 + \sqrt{15}}{4 + \sqrt{15}}\):
\[
\frac{1}{4 - \sqrt{15}} \times \frac{4 + \sqrt{15}}{4 + \sqrt{15}}
\]
This approach results in the denominator becoming a difference of squares, allowing for rationalization.
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