Square root
- 1. Square Numbers & Square Roots Perfect Squares
- 2. 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.
- 4. Square Numbers • 1 x 1 = 1 • 2 x 2 = 4 • 3 x 3 = 9 • 4 x 4 = 16
- 5. Square Numbers • 1 x 1 = 1 • 2 x 2 = 4 • 3 x 3 = 9 • 4 x 4 = 16 Activity: Calculate the perfect squares up to 152 …
- 6. Square Numbers • 1 x 1 = 1 • 2 x 2 = 4 • 3 x 3 = 9 • 4 x 4 = 16 • 5 x 5 = 25 • 6 x 6 = 36 • 7 x 7 = 49 • 8 x 8 = 64 9 x 9 = 81 10 x 10 = 100 11 x 11 = 121 12 x 12 = 144 13 x 13 = 169 14 x 14 = 196 15 x 15 = 225
- 7. Activity: Identify the following numbers as perfect squares or not. i. 16 ii. 15 iii. 146 iv. 300 v. 324 vi. 729
- 8. 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
- 9. Squares & Square Roots Square Root
- 10. Square Numbers • One property of a perfect square is that it can be represented by a square array. • Each small square in the array shown has a side length of 1cm. • The large square has a side length of 4 cm. 4cm 4cm 16 cm2
- 11. Square Numbers • The large square has an area of 4cm x 4cm = 16 cm2 . • The number 4 is called the square root of 16. • We write: 4 = 16 4cm 4cm 16 cm2
- 12. Square Root • A number which, when multiplied by itself, results in another number. • Ex: 5 is the square root of 25. 5 = 25
- 13. Finding Square Roots • We can use the following strategy to find a square root of a large number. 4 x 9 = 4 x 9 36 = 2 x 3 6 = 6
- 14. Finding Square Roots • We can factor large perfect squares into smaller perfect squares to simplify. 4 x 9 = 4 9 36 = 2 x 3 6 = 6
- 15. Finding Square Roots • Activity: Find the square root of 256 256 = 4 x 64 = 2 x 8 = 16
- 16. Squares & Square Roots Estimating Square Root
- 22. Estimating Square Roots 27 = ? Since 27 is not a perfect square, we have to use another method to calculate it’s square root.
- 23. 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.
- 24. 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.
- 25. Estimating Square Roots • Example: 27 25 3530 What are the perfect squares on each side of 27? 36
- 26. Estimating Square Roots • Example: 27 25 3530 27 5 6 half Estimate 27 = 5.2 36
- 27. Estimating Square Roots • Example: 27 Estimate: 27 = 5.2 Check: (5.2) (5.2) = 27.04