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,...
Related questions
Question
![**Radical Expressions**
**Problem 11:**
\[
\sqrt{40} - \sqrt{90}
\]
This problem involves subtracting two radical expressions. The goal is to simplify each radical to its simplest form before subtracting.
- **Simplifying the radicals:**
- \(\sqrt{40}\) can be broken down to \(\sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\).
- \(\sqrt{90}\) can be simplified to \(\sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\).
- **Subtracting the simplified radicals:**
- Combine like terms: \(2\sqrt{10} - 3\sqrt{10} = -1\sqrt{10}\).
So, the simplified expression is \(-\sqrt{10}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc37dbff0-e053-476c-a940-a199db5d9106%2F2274d803-5da9-4175-b419-bafa636e67c6%2Feqyu6a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Radical Expressions**
**Problem 11:**
\[
\sqrt{40} - \sqrt{90}
\]
This problem involves subtracting two radical expressions. The goal is to simplify each radical to its simplest form before subtracting.
- **Simplifying the radicals:**
- \(\sqrt{40}\) can be broken down to \(\sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\).
- \(\sqrt{90}\) can be simplified to \(\sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\).
- **Subtracting the simplified radicals:**
- Combine like terms: \(2\sqrt{10} - 3\sqrt{10} = -1\sqrt{10}\).
So, the simplified expression is \(-\sqrt{10}\).
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