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Adding and Subtracting Radicals quiz

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  • What are 'like radicals' when adding or subtracting radical expressions?
    Like radicals have the same radicand and the same index, allowing them to be combined.
  • Can you add radicals with different indexes, such as a square root and a cube root?
    No, you cannot combine radicals with different indexes; only those with the same index and radicand can be added or subtracted.
  • How do you combine 2√x and 4√x?
    You add the coefficients to get 6√x, since both terms have the same radicand and index.
  • What mistake do students often make when adding √7 + √7?
    Students sometimes incorrectly write √7 + √7 as √14, but this is not correct; you should add the coefficients to get 2√7.
  • What should you do if radicals are not like each other, such as √5 and √20?
    You should simplify the radicals first, factoring out perfect powers, to see if they can become like radicals.
  • How do you simplify √20?
    √20 can be written as √4 × √5, which simplifies to 2√5.
  • After simplifying √5 + 2√5, what is the result?
    You add the coefficients to get 3√5.
  • How do you simplify √18?
    √18 can be written as √9 × √2, which simplifies to 3√2.
  • How do you simplify √50?
    √50 can be written as √25 × √2, which simplifies to 5√2.
  • What is the result of 5√2 - 3√2?
    Subtract the coefficients to get 2√2.
  • What is the result of 3√2 + 5√2?
    Add the coefficients to get 8√2.
  • Can you combine radicals by merging their radicands, such as √7 + √7 = √14?
    No, you cannot merge radicands; you must add the coefficients if the radicals are alike.
  • What is the first step when adding or subtracting radicals that are not alike?
    The first step is to simplify each radical by factoring out perfect powers.
  • If you have 3√5 + 4√5, what is the simplified form?
    The simplified form is 7√5.
  • Why is simplifying radicals important before combining them?
    Simplifying radicals can turn unlike radicals into like radicals, allowing you to combine them.