Squares & Square Roots (Practice - Estimating Radicals)

Squares & Square Roots Perfect Squares Lesson 2.1  Vocabulary  The number of square units that can form a square is called a perfect square.  The number of cube units that can form a cube is called a perfect cube.  The square root of the area of the square (perfect...

Squares & Square Roots Perfect Squares Lesson 2.1  Vocabulary  The number of square units that can form a square is called a perfect square.  The number of cube units that can form a cube is called a perfect cube.  The square root of the area of the square (perfect square) is the length of the side of the square.  The cube root of the volume of a cube (perfect cube) is the length of each side of the cube.  Square Number  Also called a “perfect square”  A number that is the square of a whole number  Can be represented by arranging objects in a square. Square Numbers  Square Numbers 1x1=1 2x2=4 3x3=9 4x4= 16  Square Numbers 1x1=1 2x2=4 3x3=9  4 x 4 = 16 Activity: Calculate the perfect squares up to 152…  Square Numbers 1x1=1  9 x 9 = 81 2x2=4  10 x 10 = 100 3x3=9  11 x 11 = 121  12 x 12 = 144  4 x 4 = 16  13 x 13 = 169  5 x 5 = 25  14 x 14 = 196  6 x 6 = 36  15 x 15 = 225  7 x 7 = 49  8 x 8 = 64  Activity: Identify the following numbers as perfect squares or not. i. 16 ii. 15 iii. 146 iv. 300 v. 324 vi. 729  Activity: Identify the following numbers as perfect squares or not. i. 16 = 4 x 4 ii. 15 iii. 146 iv. 300 v. 324 = 18 x 18 vi. 729 = 27 x 27  Squares & Square Roots Square Root  Square Numbers One property of a perfect square is that it can be represented by a 4cm square array. Each small square in the 4cm 16 cm2 array shown has a side length of 1cm. The large square has a side length of 4 cm.  Square Numbers The large square has an area of 4cm x 4cm = 16 4cm cm2. 4cm 16 cm2 The number 4 is called the square root of 16. We write: 4= 16  Square Root  A number which, when multiplied by itself, results in another number.  Ex: 5 is the square root of 25. 5 = 25  Finding Square Roots We can use the following strategy to find a square root of a large number. 4x9 = 4 x 9 36 = 2 x 3 6 = 6  Finding Square Roots 4x9 = 4 9 36 = 2 x 3 6 = 6 We can factor large perfect squares into smaller perfect squares to simplify.  Finding Square Roots  Activity: Find the square root of 256 256 = 4 x 64 =2 x 8 = 16  Squares & Square Roots Estimating Square Root  Estimating Square Roots 25 = ?  Estimating Square Roots 25 = 5  Estimating Square Roots 49 = ?  Estimating Square Roots 49 = 7  Estimating Square Roots 27 = ?  Estimating Square Roots 27 = ? Since 27 is not a perfect square, we have to use another method to calculate it’s square root.  Estimating Square Roots Not all numbers are perfect squares. Not every number has an Integer for a square root. We have to estimate square roots for numbers between perfect squares.  Estimating Square Roots To calculate the square root of a non-perfect square 1. Place the values of the adjacent perfect squares on a number line. 2. Interpolate between the points to estimate to the nearest tenth.  Estimating Square Roots Example: 27 What are the perfect squares on each side of 27? 25 30 35 36  Estimating Square Roots Example: 27 half 5 6 25 30 35 36 27 Estimate 27 = 5.2  Estimating Square Roots Example: 27  Estimate: 27 = 5.2  Check: (5.2) (5.2) = 27.04  ASSIGNMENT 2.1 =9 =14 =7 =15 =11 =4 =2 =6 =8 ASSIGNMENT 2.1 QUIZ 2.1. Complete the table below Perfect Exponential Square root Square Form Example: 20 x 20 20 400 1. _______ 28 x 28 28 2. _______ 4x4 4 100 3. _______ 10 4. _______ 23 x 23 5. _______ 441 6. _______ 7. _______ 8. _______ 9. _______ 25 10. _______ 11. _______ 9 1089 12. _______ 13. _______ QUIZ 2.1 Complete the table below Perfect Square Exponential Form Square root Example: 400 20 x 20 20 1. 784 28 x 28 28 2. 16 4x4 4 100 3. 10 x 10 10 4. 529 23 x 23 5. 23 441 6. 21 x 21 7. 21 8. 625 9. 25 x 25 25 10. 81 11. 9 x 9 9 1089 12. 33 x 33 13. 33 2500 14. 50 x 50 15. 50  Vocabulary  The number of square units that can form a square is called a perfect square.  The number of cube units that can form a cube is called a perfect cube.  The square root of the area of the square (perfect square) is the length of the side of the square.  The cube root of the volume of a cube (perfect cube) is the length of each side of the cube. perfect cubes & cube roots Learning Check What can you say about the square of negative numbers? squaring a negative number yields the same value as squaring its positive counterpart. What can you say about the cubes of negative numbers? when we cube a negative number we get a negative number QUIZ 2.2. Complete the table below Number Square root of a Cube root of a number number Example: 8 Not perfect 2 square 1. 729 2. 1331 3. -27 4. 1/4 5. 9/25 6. 3375 7. -8 8. 21952 9. 784 QUIZ 2.2. Complete the table below Number Square root of a Cube root of a number number Example: 8 Not perfect 2 square 1. 729 2. 1331 3. -27 4. 1/4 5. 9/25 6. 3375 7. -8 8. 21952 9. 784 QUIZ 2.2. Complete the table below Number Square root of a Cube root of a number number Example: 8 2 1. 729 27 9 2. 1331 Not perfect 11 square 3. -27 Not perfect -3 square 4. 1/4 1/2 Not perfect cube 5. 9/25 3/5 Not perfect cube 6. 3375 Not perfect 15 square QUIZ 2.2. Complete the table below Number Square root of a Cube root of a number number Example: 8 Not perfect 2 square 1. 49 2. 121 3. -27 4. 1/4 5. 9/25 6. 216 7. -8 8. 324 9. 512  Number Square root of a Cube root of a number number Example: 8 Not perfect 2 square 9 3 Not perfect cube QUIZ 2.2. Complete the table below Number Square root of a Cube root of a number number Example: 8 2 1. 49 7 Not perfect cube 2. 121 11 Not perfect cube 3. -27 Not perfect -3 square 4. 1/4 1/2 Not perfect cube 5. 9/25 3/5 Not perfect cube 6. 216 Not perfect 6