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• • • • • • …√ …Perfect Squares...Square Roots…Roots…𝑥𝑥 2 … The square root of all perfect squares will always be rational A perfect square can NEVER be negative o A perfect square is the PRODUCT of multiplying an integer by itself However, a root can be negative or positive o A root is the ANSWER to a square root problem o It is the ACTUAL # being multiplied TO ITSELF The fancy checkmark is a called a ‘radical’ o √9 This is called “radical 9” OR “the square root of 9” 9 is a perfect square The solution is ± 3 The “is it a perfect square?” SHORTCUT: o EVEN amount of 0’s AND has a perfect square in the beginning 900—perfect (9 is a perfect square and it has an even amount of 0’s) 4,000—NOT PERFECT (4 is a perfect square BUT IT IS AN ODD AMOUNT OF 0’s) Remember: o A perfect SQUARE will NEVER be a NEGATIVE o The square root of a perfect square is rational (Q) √# --- # comes from the ‘Perfect Square’ column below o The square root of any whole number that is NOT a perfect square is IRRATIONAL (I) √# --- # is not from the perfect square column (it’s in-between 2 perfect squares) Root 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 Root Squared 𝑥𝑥 2 Square Root √ 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 =196 152 =225 202 =400 252 =625 302 =900 √1=±1 √4=±2 √9=±3 √16=±4 √25=±5 √36=±6 √49=±7 √64 =±8 √81=±9 √100=±10 √121=±11 √144=±12 √169=±13 √196=±14 √225=±15 √400=±20 √625=±25 √900=±30 Perfect Square 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 400 625 900