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
![**Radical Expressions**
**Problem 10:**
\[ 3\sqrt{125} - \sqrt{500} \]
This problem involves simplifying radical expressions by breaking them down into their simplest forms. To simplify each radical, factor the numbers under the root sign into primes and separate out squares.
- For \(\sqrt{125}\), since \(125 = 5 \times 5 \times 5\), it can be simplified to \(5\sqrt{5}\).
- For \(\sqrt{500}\), since \(500 = 2 \times 5 \times 5 \times 5 \times 2\), it can be simplified to \(10\sqrt{5}\).
The new expression becomes:
\[ 3(5\sqrt{5}) - 10\sqrt{5} \]
\[ = 15\sqrt{5} - 10\sqrt{5} \]
\[ = 5\sqrt{5} \]
The final answer is \(5\sqrt{5}\).
This exercise helps in understanding how to handle and simplify radicals, which is a crucial skill in algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc37dbff0-e053-476c-a940-a199db5d9106%2F49dfac4f-6709-4ecd-8d7d-1a60a3321829%2F9nleppn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Radical Expressions**
**Problem 10:**
\[ 3\sqrt{125} - \sqrt{500} \]
This problem involves simplifying radical expressions by breaking them down into their simplest forms. To simplify each radical, factor the numbers under the root sign into primes and separate out squares.
- For \(\sqrt{125}\), since \(125 = 5 \times 5 \times 5\), it can be simplified to \(5\sqrt{5}\).
- For \(\sqrt{500}\), since \(500 = 2 \times 5 \times 5 \times 5 \times 2\), it can be simplified to \(10\sqrt{5}\).
The new expression becomes:
\[ 3(5\sqrt{5}) - 10\sqrt{5} \]
\[ = 15\sqrt{5} - 10\sqrt{5} \]
\[ = 5\sqrt{5} \]
The final answer is \(5\sqrt{5}\).
This exercise helps in understanding how to handle and simplify radicals, which is a crucial skill in algebra.
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