Presentation on theme: "Math fact: The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect square e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16."— Presentation transcript:
1Math fact:The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect squaree.g. 1+3=4, 1+3+5=9, =16
2Example 1: Estimating Square Roots of Numbers The 55 is between two integers. Name the integers. Explain your answer.5536, 49, 64, 81List perfect squares near 55.49 < 55 < 64Find the perfect squares nearest 55.49 < 55 < 64Find the square roots of the perfect squares.7 < 55 < 855 is between 7 and 8 because 55 is between 49 and 64.
3Example 2: Approximating Square Roots to the Nearest Hundredth Approximate √135 to the nearest hundredth.Step 1 Find the value of the whole number.121 < 135 < 144Find the perfect squares nearest 135.√121 <√135 <144√Find the square roots of the perfect squares.11 <135< 12√The number will be between 11 and 12.The whole number part of the answer is 11.
4Example 2 ContinuedApproximate √135 to the nearest hundredth.Step 2 Find the value of the decimal.Find the difference between the given number, 135, and the lower perfect square.135 – 121 = 14Find the difference between the greater perfect square and the lower perfect square.144 – 121 = 231423Write the difference as a ratio.Divide to find the approximate decimal value.14 ÷ 23 ≈ 0.609
5Approximate √135 to the nearest hundredth. Example 2 ContinuedApproximate √135 to the nearest hundredth.Step 3 Find the approximate value.Combine the whole number and decimal.=≈ 11.61Round to the nearest hundredth.The approximate value of to the nearest hundredth is
6Example 3: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find Round to the nearest tenth.600 ≈ …Use a calculator.600 ≈ 24.5Round to the nearest tenth.600 rounded to the nearest tenth is 24.5.