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Square Roots in College Algebra 22

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  • What is a square root of a number?

    A square root of a number is a value that, when squared, equals the original number.

  • How many square roots does a positive real number have?

    A positive real number has two square roots: one positive (principal root) and one negative.

  • What are the square roots of 9?

    The square roots of 9 are 3 (principal root) and -3 because both satisfy \(x^2=9\).

  • What is the principal square root?

    The principal square root is the positive square root of a number.

  • Why does 9 have two square roots?

    Because both 3 and -3 squared equal 9, so both satisfy the definition of square roots.

  • If \(x^2=25\), what are the values of \(x\)?

    \(x=5\) and \(x=-5\) are the two square roots of 25.

  • Does zero have two square roots?

    Zero has one square root: 0, since \(0^2=0\).

  • Can negative numbers have real square roots?

    Negative numbers do not have real square roots because no real number squared is negative.

  • What does it mean if a number is a principal root?

    It means it is the non-negative square root of a number.

  • How to verify if a number is a square root of another number?

    Square the candidate number and check if the result equals the original number.