The document discusses square roots and real numbers. It defines square roots as the number that when multiplied by itself equals the original number. Numbers with whole number square roots are called perfect squares. Most numbers are not perfect squares and have irrational square root values that are non-terminating decimals. The combination of rational and irrational numbers make up the set of real numbers. The document provides examples of finding square roots with and without a calculator and identifying the whole number a square root lies between.

1. Section 2.7 Square Roots and Real Numbers

2. By definition  25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that  25 = 5 Numbers like 25, which have whole numbers for their square roots, are called perfect squares

3. Perfect square Square root 1  1 = 1 4  4 = 2 9  9 = 3 16  16 = 4 25  25 = 5 36  36 = 6 49  49 = 7 64  64 = 8 81  81 = 9 100  100 = 10 121  121 = 11 144  144 = 12 169  169 = 13 196  196 = 14 225  225 = 15 Perfect square Square root

4. Every whole number has a square root Most numbers are not perfect squares, and so their square roots are not whole numbers. Most numbers that are not perfect squares have square roots that are irrational numbers Irrational numbers can be represented by decimals that do not terminate and do not repeat Rational + Irrational = REAL Numbers

9. Simplify the following expressions =  4 81 2 9  4  81 =  1 36  1 144 – = 1 6 1 12 – = 2 12 1 12 – = 1 12

10. Graphing real numbers The graph of a number is a dot placed where the number would be on the number line 0 5 10 -5 -10 Graph the number: 3 1 2 0 5 10 -5 -10 Graph the number: -8.5