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Mathematical Roots Square Numbers A square is a shape that has equal side lengths and 4 right angles. To find the area of a square (space inside), square the length of the sides (multiply side length side length). 3 Example: Another Example: So, “if there is a pair….there is a square”. 3 A perfect square is made from integers (... − 3, −2, −1, 0, 1, 2, 3...) . You should memorize the following perfect squares in addition to their opposites (like 2 and –2) Square Roots To square root a number you have to “undo the square”. The square root of a number is one of the two equal numbers (factors) that are multiplied together to get the number. 16 = 4 • 4 = 4 Example (positive square root): Example (negative square root): Example (both square roots): Try: ± 25 = − 16 = −4 • −4 = −4 ± 16 = ± 4 • 4 = ±4 ± 144 = −16 = ± x2 = Square Roots of Fractions Example: Try: 81 100 4 2•2 2 1 = = = 16 4•4 4 2 36 64 Solving Equations with Square Roots Try: y 2 = Examples: 4 25 z 2 = 0.09 x 2 = 49 x 2 = 49 x • x = 7• 7 x = 7 Cube Roots Here we have to “undo” a number that is cubed. A cubed number is a number raised to the power of 3 or a number multiplied by itself 3 times. Example 2 • 2 • 2 = 8 (8 is a “perfect cube); “if there is a triple, there is a cube” The Perfect Cubes (0-10) 03 33 13 23 0 1 8 27 53 125 43 64 63 216 73 343 83 512 When we do a “cube root” we undo a “triple”. Example 3 64 = 3 4 • 4 • 4 = 4 Try: 3 3 125 Solving Equations with Cube Roots 3 x 3 = 8 3 x 3 = 3 8 3 x• x• x = 3 2•2•2 x = 2 Try: x = 343 −27 93 729 10 3 1000