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Square Roots and Cube Roots 4.6 Perfect Squares •1 •4 •9 • 16 • 25 • 36 • 49 • 64 • 81 • 100 • 121 • 144 • 169 • 196 • 225 Square Root • A square root of a number is one of its two equal factors. • Notation: radical sign is used to indicate a nonnegative square root. Positive and Negative Signs 36 6 36 1 36 6 36 6 36 no real solution Find each square root 1.) 64 8 2.) 121 11 3.) 256 16 4.) 9 no real solution Estimate to the Nearest Integer • For numbers that are not perfect squares, find the two perfect square the number is between. • Graph the square root on the number line to determine which perfect square it is closest to. Estimate the nearest Integer 1.) 60 49 60 64 7 60 8 8 2.) 18 16 18 25 4 18 5 4 Cube Roots • A cube root of a number is one of its three equal factors 3 • If x y then 3 y Perfect Cube Roots •1 •8 •27 •64 •125 •216 •343 •512 •729 •1000 Every Integer has exactly one cube root • The cube root of a positive number is positive • The cube root of zero is zero • The cube root of a negative number is negative Find the Cube Root 3 1.) 125 5 2.) 3 729 9 Estimate to the nearest integer 2.) 39 1.) 3 72 3 64 3 72 3 125 3 3 27 3 39 3 64 4 72 5 3 39 4 4 3 3 3 Homework Page 172 (16-38) even