Sets
Set Operations
4 Topics
Exponents and Exponential Expressions
Polynomial Arithmetic
Factoring
Factoring Quadratic Expressions
2 Topics
Rational Expressions
Arithmetic with Rational Expressions
3 Topics
Radical Expressions
Simplifying Radical Expressions
4 Topics
Rationalizing Denominators
2 Topics
Functions Basics
Domains and Ranges of Functions
2 Topics
New Functions Constructed From Old
Piecewise-Defined Functions
2 Topics
Linear Functions
Quadratic Functions
Solving Quadratic Equations
3 Topics
Exponential Functions
Exponential Functions Basics
2 Topics
Logarithms
Logarithms
4 Topics
Adding, Subtracting, and FOILing with Radical Expressions
Mini Lecture Video
Key Takeaways
- When given a product, sum, or difference involving radical expressions, all the usual arithmetical rules apply!
- For example, for combining like-terms, \(\sqrt{2x}+5\sqrt{2x}=6\sqrt{2x}\).
- Occasionally, you will need to simplify radicals before combining like-terms.
- For example, you can FOIL expressions like \((\sqrt{2x}-\sqrt{3x})(\sqrt{2x}+\sqrt{3x})\)
- For example, for combining like-terms, \(\sqrt{2x}+5\sqrt{2x}=6\sqrt{2x}\).
- All that needs to be considered in addition to normal arithmetic rules (such as the above) is what happens when you multiply radicals.
Several examples follow; give ’em a try!
Try the Following!
Perform the given arithmetical operations
Solution: \(11\sqrt{2x}\)
Solution: \(8\sqrt[3]{3x}\)
Solution: \(22\sqrt{2y}\)
Solution: \(1\)
Solution: \(\sqrt{10}-\sqrt{15}+\sqrt{6}-3\)
Solution: \(8|x|-4\sqrt{3x}+4\sqrt{5x}-2\sqrt{15}\)
Solution: \(15+10\sqrt{2}\)
Solution: \(4\). yup. just \(4\).
Solution: \(6+2\sqrt[3]{3}\)