Math 6/7 NOTES (4.3) Name: Squares, Perfect Squares ...

1 Math 6/7 NOTES ( ) Name: _____ Squares , Perfect Squares & square Roots Squares Continue the pattern of square tiles until you reach 5 tiles on each side. Complete the following table: Tiles on a Side 1 2 3 4 5 Total Number of Tiles in The square Arrangement Suppose a square arrangement has 36 tiles. How many tiles are on a side? _____ The product of a number and itself is the _____ of the number. 4 : four to the second power or four squared 4 = 4 4 = 16 units 4 units 4 units Write each power as a product of the same factor. 1) 6 2) 13 3) ( 4) Write each product in the exponential form. 4) 17 17 5) ( 2) ( 2) 6) 11 11 Find the square of each number 7) 3 8) 8 9) 4 10) 5 11) 12) 13) 3p 14) 15) 12m Perfect Squares Numbers such as 1, 4, 9, 16, and 25 are called _____, because they are Squares of _____.

2 Memorize the Perfect Squares through 400: 1 = 6 = 11 = 16 = 2 = 7 = 12 = 17 = 3 = 8 = 13 = 18 = 4 = 9 = 14 = 19 = 5 = 10 = 15 = 20 = square Roots A _____ of a number is one of its two equal factors. 4 4 = 16, so 4 is the _____ of 16. The symbol , called a _____ , is used to show a _____square root . Find each square root . times itself gives you 81? (? ? = 81) Every positive number has two square roots: A POSITIVE root and a NEGATIVE root . The symbol for the positive square root is: shows the _____ square root of 25: _____ The symbol for negative square root is: shows the _____ square root of 25: _____ shows both _____ and _____ square roots of 25.

3 = 5 and 5!! What is times itself gives you 25? (? ? = 25) _____ You Try: If n = a, then n = c = 9 b = 169 m = 289 c = b = m = c = b = m = To place 25 chairs in a square arrangement, how many chairs should be in each row? Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should she plant in each row? Area of a square is equal to the square of the length of a side. A = s A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is each side of the portrait? The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square .

4 Solve each equation d = 64 x = 121 n = 169 What if it is not a Perfect square ? The square root of a number that is not a Perfect square falls between two _____ whole numbers. Step 1 Determine whether a number is a Perfect square . 1. Is the number 29 a Perfect square ? Is there a whole number which can be squared to equal 29? _____ Step 2 Find the two consecutive whole numbers between which the lies. 2. The number 25 is the closest Perfect square _____ than 29. What is ? _____ 3. The number 36 is closest Perfect square greater than 29. What is ? _____ 4. lies between and . What are the two consecutive whole numbers between which lies? _____ Find the two consecutive whole numbers between which the square root of a given number lies. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ Area = 144 square inches Area = 49 square feet Area = 324 square meters