Questions and Answers
What is the result of combining the expression $6√7 + 5√7 - 3√7$?
What is the simplified expression of $5√6 + 3√7 + 4√7 - 2√6¼$?
3√6 + 7√7
What should you do when asked to simplify each expression?
Simplify each radical first and then combine.
Simplify the expression $2√50 - 3√32$.
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What is the final result when combining $3√27 + 5√48$?
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Study Notes
Combining Radicals Overview
- Radicals can be combined when they have the same root and coefficient.
- Simplifying radicals helps to combine them more effectively.
Example of Combining Radicals
- 6√7 + 5√7 - 3√7 simplifies to 8√7, showing addition and subtraction of like radicals.
Additional Example with Multiple Radicals
- 5√6 + 3√7 + 4√7 - 2√6 simplifies to 3√6 + 7√7, highlighting the importance of organizing similar radicals.
Simplification Steps
- For expressions like 2√50 - 3√32, first break down the radicals:
- Rewrite as 2√(252) - 3√(162).
- Simplify to 25√2 - 34√2 leading to 10√2 - 12√2.
- Final result is -2√2.
Further Example of Combining Radicals
- In 3√27 + 5√48, the expression simplifies as follows:
- Rewrite as 3√(93) + 5√(163).
- Simplify into 33√3 + 54√3 which equals 9√3 + 20√3.
- Combined result is 29√3.
General Rule for Simplifying Radicals
- Always simplify each radical before attempting to combine them.
- Look for perfect squares, cubes, or other roots in the radical to make simplification easier.
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Description
These flashcards provide practice on combining and simplifying radical expressions. Each card contains an expression and its simplified form, guiding you through the process of radical simplification. Perfect for students looking to master this algebraic concept.
