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Square Roots and Cube Roots

Square Roots and Cube Roots. September 17, 2013. Square Root. The square root of a nonnegative number is a number that, when multiplied by itself, is equal to that nonnegative number. Square roots have positive and negative solutions. The symbol represents a square root.

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Square Roots and Cube Roots

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  1. Square Roots and Cube Roots September 17, 2013

  2. Square Root The square root of a nonnegative number is a number that, when multiplied by itself, is equal to that nonnegative number. Square roots have positive and negative solutions. The symbol represents a square root. Taking the square root of a number is the opposite, or inverse, of squaring the number.

  3. Solving Square Roots EXAMPLE #1 You can solve an equation by taking the square root of both sides. = 100 = x = ⟶ 10 x 10 = 100 and -10 x -10 = 100 x = ± 10

  4. Solving Square Roots EXAMPLE #2 The number under the square root symbol is called the radicand. If the radicand is not a perfect square, the square root is irrational. = 5 = ⟶ 5 is not a perfect square x = x = ± x = ± 2.23606…

  5. Cube Root To find the cube root of a number, find the number that, when multiplied by itself two times (a total of three factors), is equal to that number. The symbol represents a cube root. Taking the cube root of a number is the opposite, or inverse, of cubing a number (raising a number to the third power).

  6. Solving Cube Roots EXAMPLE #1 You can solve an equation by taking the cube root of both sides. = 125 = x = ⟶ 5 x 5 x 5 = 125 x = 5

  7. Practice Problem 1 • Solve for x • = 169

  8. Practice Problem 2 • Approximate the value of x • = 50

  9. Practice Problem 3 • Solve for x • = 216

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