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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 \((\sqrt{2x}-\sqrt{3x})(\sqrt{2x}+\sqrt{3x})\)
  • 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: \(6+2\sqrt[3]{3}\)

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