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Estimating Square Roots and Cube Roots to the nearest tenth!

Estimating Square Roots and Cube Roots to the nearest tenth!. Estimate √28 to the nearest tenth. First find the two perfect squares √28 is between. √25 = 5 and √36 = 6 so…….. √28 is between 5 & 6. Now…… decide which it is closer to √25 √28 √36

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Estimating Square Roots and Cube Roots to the nearest tenth!

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  1. Estimating Square Roots and Cube Roots to the nearest tenth!

  2. Estimate √28 to the nearest tenth. First find the two perfect squares √28 is between. √25 = 5 and √36 = 6 so…….. √28 is between 5 & 6. Now…… decide which it is closer to √25 √28 √36 so, √28 is closer to √25 3 8

  3. Since √28 is closer to √25 and √25 = 5 Start your guess and check with a number closer to 5.0 5.2 X 5.2 104 2600 27.04 5.3 X 5.3 159 2650 28.09 √28 is between 5.2 & 5.3 But………. Which is it closer to? 5.3 • 28.00 • - 27.04 • 0.96 • 28.09 • - 28.00 • 0.09

  4. Estimate √73 to the nearest tenth. Find the two perfect squares √73 is between. √64 = 8 and √81 = 9 so…….. √73 is between 8 & 9. Now…… decide which it is closer to √64 √73 √81 so, √73 is almost the same distance from both 9 8

  5. Since √73 is almost the same distance from both… Start your guess and check with a number in the middle. √73 is between 8.5 & 8.6 But………. Which is it closer to? 8.5 X 8.5 425 6800 72.25 8.6 X 8.6 516 6880 73.96 8.5 • 73.00 • - 72.25 • 0.75 • 73.96 • - 73.00 • 0.96

  6. Estimate √139 to the nearest tenth. Find the two perfect squares √139 is between. √121 = 11 and √144 = 12 so…….. √139 is between 11 & 12. Now…… decide which it is closer to √121 √139 √144 so, √139 is closer to √144 18 5

  7. Since √139 is closer to √144 and √144 = 12 Start your guess and check with a number closer to 12.0 √139 is between 11.7 & 11.8 But………. Which is it closer to? 11.8 X 11.8 944 1180 11800 139.24 11.7 X 11.7 819 1170 11700 136.89 11.8 • 139.24 • - 139.00 • 0.24 • 139.00 • - 136.89 • 2.11

  8. Estimate ³√29 to the nearest tenth. First find the perfect cube ³√29 is between. ³√27 = 3and ³√64 = 4 so…….. ³√29 is between 3 & 4. Now…… decide which it is closer to ³√27 ³√29 ³√64 so, ³√29 is closer to ³√27 35 2

  9. Since ³√29 is closer to ³√27 and ³√27 = 3 Start your guess and check with a number closer to 3.0 ³√29 is between 3.0 & 3.1 But………. Which is it closer to? 3.1 X 3.1 31 930 9.61 X 3.1 361 28830 29.191 3.0 X 3.0 00 900 9.00 X 3.0 000 27000 27.000 • 29.191 • - 29.000 • 0.191 • 29.00 • - 27.00 • 2.00 3.1

  10. Estimate ³√103 to the nearest tenth. First find the perfect cube ³√103 is between. ³√64 = 4 and ³√125 = 5 so…….. ³√103 is between 4 & 5. Now…… decide which it is closer to ³√64 ³√103 ³√125 so, ³√103 is almost the same distance from both 22 39

  11. Since ³√103 is almost the same distance from both… Start your guess and check with a number in the middle. ³√103 is between 4.6 & 4.7 But………. Which is it closer to? 4.6 X 4.6 276 1840 21.16 X 4.6 12696 84640 97.336 4.7 X 4.7 329 1880 22.09 X 4.7 15463 88360 103.823 • 103.000 • - 97.336 • 5.664 103.823 -103.000 0.823 4.7

  12. Homework Time!!

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