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7th Grade Chapter 10.2 Estimating Square Roots While every number (N) has a square, not every number has a perfect Square Root. PERFECT SQUARES are WHOLE Numbers: 12 1 22 4 32 9 42 16 52 25 62 36 72 49 82 64 92 81 102 100 112 121 122 144 132 169 142 Etc. 196 What is the Square Root of 22? √𝟐𝟐 Since 22 is between 16 and 25, the square root of 22 has to be between 4 and 5. 16 < 22 < 25 So √𝟏𝟔 < √𝟐𝟐 < √𝟐𝟓 or 4 < ? < 5. Since 22 is closer to 5 (3 away) compared to 16 (6 away), the Square Root will be closer to 5! Estimate √𝟖𝟓 So √𝟖𝟏 < √𝟖𝟓 < √𝟏𝟎𝟎 or 9 < ? < 10. After an accident, a police offer can estimate the speed (S) of a care before it skidded to a stop. They use the formula: 𝑠= √𝟑𝟎 ∗ 𝒅 ∗ 𝒇 where s is the speed in Miles Per Hour, d is the length of the skid marks in feet and f is a value that depends on weather conditions. (Historic data collection). What is the APPROXIMATE speed of a car that produced skid marks 90’ long with a f value of 1.2? 𝑠 ≈ √𝟑𝟎 ∗ 𝒅 ∗ 𝒇 or 𝑠 ≈ √𝟑𝟎 ∗ 𝟗𝟎 ∗ 𝟏. 𝟐 𝑺 ≈ 𝟓𝟔. 𝟗 ≈ √𝟑, 𝟐𝟒𝟎