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Adding and Subtracting Radicals quiz

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  • What are 'like radicals' in the context of adding and subtracting radicals?
    Like radicals have the same radicand and the same index, allowing them to be combined.
  • Can you add 3√7 and 2√7 together? If so, what is the result?
    Yes, you can add them because they are like radicals; the result is 5√7.
  • Why can't you add √7 and ³√7 together?
    You can't add them because they have different indexes (square root vs. cube root), so they are not like radicals.
  • What mistake do students often make when adding √7 + √7?
    Students often incorrectly write √7 + √7 as √14, but the correct answer is 2√7.
  • What should you do before adding or subtracting radicals that are not like each other?
    You should simplify the radicals by factoring out perfect powers to try to make them like radicals.
  • How do you simplify √20 before adding it to √5?
    Break down √20 into √4 × √5, which simplifies to 2√5, making it possible to combine with √5.
  • After simplifying √20 to 2√5, what is √5 + 2√5?
    The sum is 3√5.
  • How do you simplify √18 before subtracting it from 5√2?
    Break down √18 into √9 × √2, which simplifies to 3√2.
  • What is 5√2 - √18 after simplifying the radicals?
    It becomes 5√2 - 3√2, which simplifies to 2√2.
  • If you have √18 + √50, what should you do to combine them?
    Simplify both radicals: √18 = 3√2 and √50 = 5√2, then add to get 8√2.
  • Can you combine radicals with different radicands, such as √3 and √5?
    No, you cannot combine them unless you can simplify them to have the same radicand and index.
  • What is the result of 3√5 + 4√5?
    The result is 7√5.
  • Why is it important to factor out perfect powers when simplifying radicals?
    Factoring out perfect powers can turn unlike radicals into like radicals, allowing you to combine them.
  • What is the simplified form of √9 × √2?
    It simplifies to 3√2.
  • If you have 9∛x - 4∛x + 3 - √x, what is the simplified expression?
    The simplified expression is 5∛x + 3 - √x.