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California Standards

California Standards. for an integer that is not a square, determine without a calculator the two integers between which its square root lies and explain why. 55. 55 is between 7 and 8 because 55 is between 49 and 64. 49 < 55 < 64. 7 < 55 < 8.

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California Standards

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  1. California Standards for an integer that is not a square, determine without a calculator the two integers between which its square root lies and explain why.

  2. 55 55 is between 7 and 8 because 55 is between 49 and 64. 49 < 55 < 64 7 < 55 < 8 Additional Example 1: Estimating Square Roots of Numbers The 55 is between two integers. Name the integers. Explain your answer. Notes 36, 49, 64, 81 List perfect squares near 55. Find the perfect squares nearest 55. 49 < 55 < 64 Find the square roots of the perfect squares.

  3. The 80 is between two integers. Name the integers. Explain your answer. 80 80 is between 8 and 9 because 80 is between 64 and 81. 64 < 80 < 81 8 < 80 < 9 Check It Out! Example 1 Elbow Partners 49, 64, 81, 100 List perfect squares near 80. Find the perfect squares nearest 80. 64 < 80 < 81 Find the square roots of the perfect squares.

  4. The length of each side of the square is √185 . < √169 < √185 √196 13 < < 14 √185 185 is closer to 196 than to 169, so 185 is closer to 14 than 13. √185  14 Additional Example 2: RecreationApplication A Coast Guard boat searching for a lost sailboat covers a square area of 185 mi2. What is the approximate length of each side of the square area? Round your answer to the nearest mile. List perfect squares near 185. 144, 169, 196, 225 169 < 185 < 196 Find the perfect squares nearest 185. Find the square roots of the perfect squares. Each side of the search area is about 14 miles long.

  5. The length of each side of the square is √168 . < √144 < √168 √169 12 < < 13 √168 168 is closer to 169 than to 144, so 168 is closer to 13 than 12. √168  13 Check It Out! Example 2 A tent was advertised in the newspaper as having an enclosed square area of 168 ft2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot. 121, 144, 169, 196 List perfect squares near 168. 144 < 168 < 169 Find the perfect squares nearest 168. Find the square roots of the perfect squares. Each side of the tent is about 13 feet long.

  6. Approximate √135 to the nearest hundredth. √ √121 < 144 √135 < 11 < 135 < 12 √ Additional Example 3: Approximating Square Roots to the Nearest Hundredth Notes Step 1 Find the value of the whole number. Find the perfect squares nearest 135. 121 < 135 < 144 Find the square roots of the perfect squares. The number will be between 11 and 12. The whole number part of the answer is 11.

  7. Approximate √135 to the nearest hundredth. Additional Example 3 Continued Step 2 Find the value of the decimal. Find the difference between the given number, 135, and the lower perfect square. 135 – 121 = 14 Find the difference between the greater perfect square and the lower perfect square. 144 – 121 = 23 1423 Write the difference as a ratio. Divide to find the approximate decimal value. 14 ÷ 23 ≈ 0.609

  8. Approximate √135 to the nearest hundredth. The approximate value of 135 to the nearest hundredth is 11.61. Additional Example 3 Continued Step 3 Find the approximate value. Combine the whole number and decimal. 11 + 0.609 = 11.609 Round to the nearest hundredth. 11.609 ≈ 11.61

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