1. Pg. 106-108 #8-46 e, 59-60

2. 59.) C60.) A

5. Vocabulary If _________, then ___ is a ____________ of ____. –Example: Perfect Squares: –Examples: b square root a radical symbol radicand square of all the integers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

6. REAL NUMBERS Irrational NumbersRational Numbers Integers Whole Numbers -4 -27 5 016

7. Find square roots EXAMPLE 1 a.  – + 36 = The positive and negative square are 6 and – 6. roots of 36 b.  49 = The positive square root of 49 is 7. c.  4 – = The negative square root of 4 is – 2. Evaluate the expression. + – 6 7 -2

8. Find square roots EXAMPLE 1  – 1. 9 – =3  2. 25 = 5 GUIDED PRACTICE for Example 1 Evaluate the expression.  64 3. – + =8 – +  – 4. 81 = 9 –

9. Approximate a square root EXAMPLE 2 FURNITURE The top of a folding table is a square whose area is 945 square inches. Approximate the side length of the tabletop to the nearest inch. SOLUTION You need to find the side length s of the tabletop such that s 945. This means that s is the positive square root of 945. You can use a table to determine whether 945 is a perfect square. Number 2829303132 Square of number 7848419009611024 As shown in the table, 945 is not a perfect square. The greatest perfect square less than 945 is 900. The least perfect square greater than 945 is 961. 900 < 945 < 961 Write a compound inequality that compares 945 with both 900 and 961. < <  961  900  945 Take positive square root of each number. 30  945 < < 31 Find square root of each perfect square. Because 945 is closer to 961 than to 900, is closer to 31 than to 30.  945 The side length of the tabletop is about 31 inches.

10. Approximate a square root EXAMPLE 2 GUIDED PRACTICE for Example 2 Approximate the square root to the nearest integer. 5.  32 6 6.  103 10 7.  48 – – 7 8.  350 – – 19

11. Classify numbers EXAMPLE 3 Tell whether each of the following numbers is a real number, a rational number, an irrational number, an integer, or a whole number:,, –.  24  81  100 No YesNoYes NoYesNoYes Real Number ? Yes NoYes Whole Number ? Integer ? Irrational Number ? Rational Number ? Number  24  100 – –  81

12. Graph and order real numbers EXAMPLE 4, Order the numbers from least to greatest: 4 3,, –  5  13 –2.5,  9. SOLUTION Begin by graphing the numbers on a number line. 4 3 ANSWER Read the numbers from left to right: –2.5,–  5  9  13.,,,

13. Graph and order real numbers EXAMPLE 4 Tell whether each of the following numbers is a real number, a rational number, an irrational number, an integer, or a whole number:, 5.2, 0,, 4.1, Then order the numbers from least to greatest. 9.  7 9 2 – –  –  20 GUIDED PRACTICE for Examples 3 and 4 9 2 –,  7,,, –  20 0, 4.1 5.2. ANSWER

14. Graph and order real numbers EXAMPLE 4 GUIDED PRACTICE for Examples 3 and 4 No YesNoYes NoYes Real Number ? No Yes Whole Number ? Integer ? Irrational Number ? Rational Number ? Number  20  7 9 2 4.1 0 No YesNoYes No Yes – – 5.2 No Yes

15. Check Yourself Pg. 113-116 #4-40e, 47-48, 56-57