Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Problem 9: Radical Expressions
Consider the following table:
| Radical | Value |
|----------------|-------|
| \( \sqrt[3]{1000} \) | \( x \) |
| \( \sqrt[3]{27} \) | \( y \) |
| \( \sqrt[3]{z} \) | \( 5 \) |
#### Task
Find the values of \( x \), \( y \), and \( z \).
#### Explanation
1. **Cube Root of 1000**: The cube root of 1000 is the number that, when multiplied by itself three times, equals 1000. This can be calculated as:
\[
\sqrt[3]{1000} = 10
\]
Thus, \( x = 10 \).
2. **Cube Root of 27**: The cube root of 27 is the number that, when multiplied by itself three times, equals 27. This can be calculated as:
\[
\sqrt[3]{27} = 3
\]
Thus, \( y = 3 \).
3. **Finding \( z \):** Given that \( \sqrt[3]{z} = 5 \), you need to find \( z \). This means:
\[
z = 5^3 = 125
\]
Thus, the values are:
- \( x = 10 \)
- \( y = 3 \)
- \( z = 125 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0666bd56-3900-4aba-90a2-685d1b83d3e8%2F0354d075-683e-4c68-909f-8cf1b7027a6e%2F6y5zwb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 9: Radical Expressions
Consider the following table:
| Radical | Value |
|----------------|-------|
| \( \sqrt[3]{1000} \) | \( x \) |
| \( \sqrt[3]{27} \) | \( y \) |
| \( \sqrt[3]{z} \) | \( 5 \) |
#### Task
Find the values of \( x \), \( y \), and \( z \).
#### Explanation
1. **Cube Root of 1000**: The cube root of 1000 is the number that, when multiplied by itself three times, equals 1000. This can be calculated as:
\[
\sqrt[3]{1000} = 10
\]
Thus, \( x = 10 \).
2. **Cube Root of 27**: The cube root of 27 is the number that, when multiplied by itself three times, equals 27. This can be calculated as:
\[
\sqrt[3]{27} = 3
\]
Thus, \( y = 3 \).
3. **Finding \( z \):** Given that \( \sqrt[3]{z} = 5 \), you need to find \( z \). This means:
\[
z = 5^3 = 125
\]
Thus, the values are:
- \( x = 10 \)
- \( y = 3 \)
- \( z = 125 \)
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