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Introduction to Radical Expressions quiz

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  • What is the square root of 16?
    The square roots of 16 are 4 and -4, because both 4 × 4 and (-4) × (-4) equal 16.
  • What does the radical symbol (√) represent?
    The radical symbol (√) represents the principal (positive) square root of a number.
  • How do you indicate the negative square root of a number using notation?
    You place a negative sign in front of the radical symbol, like -√9, to indicate the negative square root.
  • What are the square roots of 9?
    The square roots of 9 are 3 and -3, since both squared give 9.
  • If you see √36, what is the answer?
    √36 means the principal root, which is 6.
  • What does -√36 mean?
    -√36 means the negative square root of 36, which is -6.
  • What does ±√9 mean?
    ±√9 means both the positive and negative square roots, so both 3 and -3.
  • Why can't you take the square root of a negative number in real numbers?
    Because no real number squared gives a negative result; the answer is imaginary.
  • What is the result of √(-9)?
    √(-9) is imaginary because there is no real number that squares to -9.
  • What is the difference between a negative outside and inside the radical symbol?
    A negative outside the radical is fine and gives a negative root, but a negative inside means the result is imaginary.
  • If you see -√25, what is the answer?
    -√25 is -5, the negative square root of 25.
  • What is the principal square root of 49?
    The principal square root of 49 is 7.
  • How many real square roots does a positive real number have?
    A positive real number has two real square roots: one positive (principal) and one negative.
  • What should you write if you want to indicate both square roots of a number?
    You should write ± in front of the radical, like ±√16, to indicate both roots.
  • Why is proper notation important when writing square roots?
    Proper notation distinguishes between the positive and negative roots and helps avoid errors in solving equations.