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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, meaning the number under the radical and the root are identical.
  • When can you combine radical expressions by addition or subtraction?
    You can combine radical expressions only when they are like radicals, having the same radicand and index.
  • How do you add 2√x and 4√x?
    You add the coefficients to get 6√x because both terms are like radicals.
  • 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.
  • Is √7 + √7 equal to √14? Why or why not?
    No, because you cannot combine the radicands when adding radicals; √7 + √7 equals 2√7.
  • What should you do if you are asked to add √5 and √20?
    First, simplify √20 to 2√5, then add to get 3√5 since they become like radicals.
  • How do you simplify 5√2 - √18?
    Simplify √18 to 3√2, then subtract to get 2√2.
  • What is the process for adding or subtracting radicals with different radicands?
    Simplify each radical by factoring out perfect powers to see if they can be rewritten as like radicals, then combine if possible.
  • If you have √18 + √50, what should you do before adding?
    Simplify both radicals: √18 becomes 3√2 and √50 becomes 5√2, then add to get 8√2.
  • Why is it important to check both the radicand and the index before combining radicals?
    Because only radicals with the same radicand and index can be combined; otherwise, they are not like radicals.
  • What mistake do students often make when adding radicals like √7 + √7?
    They incorrectly add the radicands to get √14, but the correct answer is 2√7.
  • How do you add 3√5 and 4√5?
    Add the coefficients to get 7√5 since both are like radicals.
  • What is the simplified form of √9 × √2?
    It simplifies to 3√2 because √9 is 3.
  • If you cannot simplify two radicals to have the same radicand and index, what should you do?
    You cannot combine them; leave the expression as is.
  • What is the general strategy for adding or subtracting radicals that are not initially like radicals?
    Simplify each radical as much as possible to see if they become like radicals, then combine their coefficients if possible.