Square Roots and Real Numbers Algebra I ~ Chapter 2-7 Square Roots and Real Numbers

SQUARE ROOTS A square root is one of two equal factors of a number. For example, one square root of 64 is 8 since 8 ∙ 8 (or 82) is 64. Another square root of 64 is -8 since -8 ∙ -8 or (-8)2 is also 64. 64 is an example of a perfect square.

Square Roots The symbol is called a radical sign and is used to indicate a nonnegative or principal square root of the expression under the radical sign.

Perfect Squares up to 15 12 = 1 62 = 36 112 = 121 12 = 1 62 = 36 112 = 121 22 = 4 72 = 49 122 = 144 32 = 9 82 = 64 132 = 169 42 = 16 92 = 81 142 = 196 52 = 25 102 = 100 152 = 225

Find each square root -4 1.) 2.) 3.) 12 (NOTE: When the question asks for just the square root as in #1, this indicates that they are looking for the principal square root, which means the nonnegative square root answer.) -4

Find each square root 1.) 2.) 3.) 15 -11

Find each square root 1.) 2.) 0.6 -0.08

Estimating Square Roots Example – Estimate Figure out which “perfect squares” falls between. In this case, falls between and , thus falling between the whole numbers 4 and 5. A good estimate would be 4.4 or 4.5 because 20 is almost between 16 and 25.

Estimating Square Roots Example – Estimate Figure out which “perfect squares” falls between. In this case, falls between and , thus falling between the whole numbers 9 and 10. A good estimate would be 9.1 or 9.2 because 83 is closer to 81 than it is to 100.

Classifying numbers by sets: 1.) 2.) 3.) 4.) Irrational Rational Integer Non-real number

Graphing Real Numbers Graph each solution set 1.) y ≥ -3 2.) a < 0

Classwork 2.7 Study Guide and Intervention Worksheet