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Warm Up

Find Square Roots and Compare Real Numbers. Warm Up. Lesson Presentation. Lesson Quiz. –. –. 3. 2.5. <. ANSWER. 19. 8. 4. 5. 21. 6. 25. ANSWER. <. ?. ?. Warm-Up. Find the square of the number. 1. 14. ANSWER. 196. 2. 16. 256. ANSWER.

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Warm Up

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  1. Find Square Roots and Compare Real Numbers Warm Up Lesson Presentation Lesson Quiz

  2. – – 3. 2.5 < ANSWER 19 8 4. 5 21 6 25 ANSWER < ? ? Warm-Up Find the square of the number. 1. 14 ANSWER 196 2. 16 256 ANSWER Complete the statements using <, >, or =.

  3. Warm-Up 5. A square room has a side length of 25 feet. What is its area? ANSWER 625 ft2

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

  5. 1. 4.   9 81 – – – = 3 2. 5 = 25 + –  64 3. + = 8 – 9 – = Guided Practice Evaluate the expression. 

  6. 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. You need to find the side length sof the tabletop such that s945. This means that sis the positive square root of 945. You can use a table to determine whether 945 is a perfect square. = 2 Example 2 FURNITURE SOLUTION

  7. < 31 30 < 900 945 961 945 < <     Example 2 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 945with both 900 and 961. Take positive square root of each number. Find square root of each perfect square.

  8. Because 945 is closer to 961 than to 900, is closer to 31 than to 30. ANSWER The side length of the tabletop is about 31 inches. 945  Example 2

  9. – – 8. 7. 5. 6. 32 48 103 350     Guided Practice Approximate the square root to the nearest integer. 6 10 – 7 – 19

  10. 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 81 – Example 3 Integer? Irrational Number? Real Number? Rational Number? Whole Number? Number  Yes No No Yes No 24 Yes Yes No Yes Yes  100 Yes Yes No Yes No

  11. Tell whether is a real number, a rational number, an irrational number, an integer, or a whole number. 9 – 2 ANSWER real number and rational number Guided Practice 9.

  12. 4 4 4 Compare and . 3 3 3 . 13 13 13    ANSWER Because is to the left of , < . Example 4 SOLUTION Graph the numbers on a number line.

  13. – ? ? (a) –2.5 7 5   14 (b) 5 ANSWER ANSWER > < Guided Practice 10. Copy and complete using < or >:

  14. Given: No fractions are irrational numbers. a. Example 5 Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. SOLUTION If-then form: If a number is a fraction, then it is not an irrational number. The statement is true.

  15. Given: All real numbers are rational numbers. b. 2  The statement is false. For example, is a real number but not a rational number. Example 5 If-then form: If a number is a real number, then it is a rational number.

  16. All square roots of perfect squares are rational numbers. 11. Guided Practice Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. If-then form: If a number is the square root of perfect square, then it is a rational number. The statement is true.

  17. All repeating decimals are irrational numbers. 12. 1 3 The statement is false. For example, 0.333… is a repeating decimal and can be written as , so it is a rational number. Guided Practice Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. If-then form: If a number is a repeating decimal, then it is an irrational number.

  18. No integers are irrational numbers. 13. Guided Practice Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false. If it is false, give a counterexample. If-then form: If a number is an integer, then it is not an irrational number. The statement is true.

  19. – 6 – 5 ANSWER ANSWER +  289 4.  620 1. – ANSWER 17 ANSWER 25 – – 2.   36 21 + – 3. Lesson Quiz Evaluate the expression. Approximate the square root to the nearest integer.

  20. 5. A square courtyard has an area of 272 square feet. What is the side length of the courtyard to the nearest foot? ANSWER 16 ft Lesson Quiz

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