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...
Related questions
Question
![**Simplify completely:**
\[
-5\sqrt{45x} + 10\sqrt{125x}
\]
**Explanation:**
To simplify the expression, let's break down the square roots using factorization.
1. **Simplify \(\sqrt{45x}\):**
- \(45x = 9 \times 5 \times x = 3^2 \times 5 \times x\)
- So, \(\sqrt{45x} = \sqrt{3^2 \times 5 \times x} = 3\sqrt{5x}\)
2. **Simplify \(\sqrt{125x}\):**
- \(125x = 25 \times 5 \times x = 5^2 \times 5 \times x\)
- So, \(\sqrt{125x} = \sqrt{5^2 \times 5 \times x} = 5\sqrt{5x}\)
Now, substitute back into the original equation:
\[
-5(3\sqrt{5x}) + 10(5\sqrt{5x})
\]
Simplify further:
\[
-15\sqrt{5x} + 50\sqrt{5x} = 35\sqrt{5x}
\]
The completely simplified expression is:
\[
35\sqrt{5x}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd044583c-5a7a-479c-b47f-e9f2bc60a85c%2F83d55208-25a5-40e4-be76-d23dc2ebab33%2Ffqwg1e_processed.png&w=3840&q=75)
Transcribed Image Text:**Simplify completely:**
\[
-5\sqrt{45x} + 10\sqrt{125x}
\]
**Explanation:**
To simplify the expression, let's break down the square roots using factorization.
1. **Simplify \(\sqrt{45x}\):**
- \(45x = 9 \times 5 \times x = 3^2 \times 5 \times x\)
- So, \(\sqrt{45x} = \sqrt{3^2 \times 5 \times x} = 3\sqrt{5x}\)
2. **Simplify \(\sqrt{125x}\):**
- \(125x = 25 \times 5 \times x = 5^2 \times 5 \times x\)
- So, \(\sqrt{125x} = \sqrt{5^2 \times 5 \times x} = 5\sqrt{5x}\)
Now, substitute back into the original equation:
\[
-5(3\sqrt{5x}) + 10(5\sqrt{5x})
\]
Simplify further:
\[
-15\sqrt{5x} + 50\sqrt{5x} = 35\sqrt{5x}
\]
The completely simplified expression is:
\[
35\sqrt{5x}
\]
Expert Solution
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