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Introduction to Radical Expressions quiz

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  • What is the relationship between squaring a number and taking its square root?
    Squaring and taking the square root are opposite operations; squaring a number and then taking the square root returns you to the original number.
  • What does the radical symbol (√) represent when written by itself?
    The radical symbol by itself represents the positive (principal) square root of a number.
  • How do you indicate the negative square root of a number using notation?
    You place a minus sign in front of the radical symbol to indicate the negative square root.
  • What are the two square roots of 9?
    The two square roots of 9 are 3 and -3.
  • If you see the expression √36, what is its value?
    The value is 6, which is the positive square root.
  • What does the expression -√36 represent?
    It represents the negative square root of 36, which is -6.
  • Why can't you take the square root of a negative number in the real number system?
    Because no real number squared results in a negative value; the result is considered imaginary.
  • What does a negative sign inside the radical symbol indicate?
    A negative inside the radical means the result is imaginary, not a real number.
  • How do you write both the positive and negative square roots of a number efficiently?
    You write ± in front of the utility radical, as in ±√9, to indicate both 3 and -3.
  • What is the square root of 16?
    The square roots of 16 are 4 and -4.
  • If you see the expression √x, what root does it refer to?
    It refers to the positive (principal) square root of x.
  • What is the result of squaring -5?
    Squaring -5 gives 25, because (-5) × (-5) = 25.
  • What is the value of √25?
    The value is 5, the positive square root.
  • What is the value of -√49?
    The value is -7, the negative square root.
  • What should you remember about negatives outside versus 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.