1 / 20

Algebra I

Algebra I. 2.7 Square Roots & Comparing Real Numbers. Vocabulary. Square Root — a number times itself to make the number you started with Radicand — the number under the radical symbol Perfect Square — the square of an integer. Vocabulary.

tashya-combs
Download Presentation

Algebra I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Algebra I 2.7 Square Roots & Comparing Real Numbers

  2. Vocabulary • Square Root — a number times itself to make the number you started with • Radicand — the number under the radical symbol • Perfect Square — the square of an integer

  3. Vocabulary • Irrational Number — a number that is not rational • Real Number — the set of all rational and irrational numbers

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

  5. 4. 1.   81 9 – – – = 3 2. 5 =  25 + –  64 3. + = 8 – 9 – = GUIDED PRACTICE Evaluate the expression. The negative square root of 9 is -3 The positive square root of 25 is 5. The positive and negative square root of 64 as 8 and – 8. The negative square root of 81 is -9

  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 s of 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 = Approximate a square root EXAMPLE 2: FURNITURE SOLUTION

  7. < 31 30 < 945 961 900 945 < <     Approximate a square root 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

  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  Approximate a square root EXAMPLE 2:

  9. 1. Number 8 5 7 6 Square of number 36 25 49 64 32  GUIDED PRACTICE Approximate the square root to the nearest integer. You can use a table to determine whether 32 is a perfect square. As shown in the table,32 is not a perfect square. The greatest perfect square less than 32 is 25. The least perfect square greater than 25 is 36.

  10. Because 32 is closer to 36 than to 25, is closer to 6 than to 5. < < < 6 5 <  32 36 25 32 32     GUIDED PRACTICE 25 < 32 < 36 Write a compound inequality that compares 32 with both 25 and 36. Take positive square root of each number. Find square root of each perfect square.

  11. 2. 103  GUIDED PRACTICE Approximate the square root to the nearest integer. You can use a table to determine whether 103 is a perfect square. As shown in the table,103 is not a perfect square. The greatest perfect square less than 103 is 100. The least perfect square greater than 100 is 121.

  12. < < < 11 10 < 103 103 103 100 121      Because 100 is closer to 103 than to 121, is closer to 10 than to 11. GUIDED PRACTICE 100< 103< 121 Write a compound inequality that compares 103 with both 100 and 121. Take positive square root of each number. Find square root of each perfect square.

  13. – 3. Number – 9 – 6 – 8 – 7 Square of number 49 36 64 81 48  GUIDED PRACTICE Approximate the square root to the nearest integer. You can use a table to determine whether 48 is a perfect square. As shown in the table,48 is not a perfect square. The greatest perfect square less than 48 is 36. The least perfect square greater than 48 is 49.

  14. – – – < < –7 < < – 6 – 48  49 48 48 36     Because 49is closer than to 36, – is closer to –7 than to –6. GUIDED PRACTICE – 36 < –48 < –49 Write a compound inequality that compares 103 with both 100 and 121. Take positive square root of each number. Find square root of each perfect square.

  15. – 4. Number – 20 – 17 – 19 – 18 Square of number 324 187 361 400 350  GUIDED PRACTICE Approximate the square root to the nearest integer. You can use a table to determine whether 48 is a perfect square. As shown in the table,350 is not a perfect square. The greatest perfect square less than 350 is 324. The least perfect square greater than 350 is 361.

  16. – – – – < < 350 350 324 361 350      Because 361 is closer than to 324, – is closer to –19 than to –18. GUIDED PRACTICE – 324 < –350 < –361 Write a compound inequality that compares –350 with both –324 and ––361. Take positive square root of each number. Find square root of each perfect square. –18 –19 < <

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

  18. , 4 4 , , Order the numbers from least to greatest: – 3 3 . , –2.5 . 13 9 5 5 13 9       ANSWER Read the numbers from left to right: –2.5, – , , , Graph and order real numbers EXAMPLE 4: SOLUTION Begin by graphing the numbers on a number line.

  19. 9 2 20  4.4 = 0  7 2.6 – = 4.1 –8 –2 –1 1 3 4 –9 –7 –6 –5 –4 –3 2 5 0 5.2 GUIDED PRACTICE Order the numbers from least to greatest: SOLUTION Begin by graphing the numbers on a number line. Read the numbers from left to right:

  20. GUIDED PRACTICE • Classify the following numbers as Real, Rational, Irrational, Integer and/or Whole:

More Related