Square Roots and Cube Roots powerpoint presentation.pptx

square root table

1. Square Roots and Cube Roots

2. Perfect Squares Perfect are squares of Natural numbers Squares They LITERALLY describe the 3 3 3 3   = 9

3. Perfect Squares                         MEMORIZE THEM 1 4 9 16 25 36 49 64 81 100 121 144

4. Words to know…      

5. SQUARE ROOTS   Taking the square root of a perfect square will give you the dimension of one side of the square 3 3 9   = 3 2

6. Square Roots UNDO Squares       2 INVERSE OPERATIONS    

7. Square Roots Squares 0² = 0 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = 100 Perfect Square Roots

8. Square Roots Positive real numbers have two square roots. Find the square roots of 16. Solution The square roots of 16 are 4 and - 4. 4 ∙ 4 = 4 2 = 16 = 4 Positive square root of 16 (–4)( – 4) = (–4) 2 = 16 = –4 Negative square root of 16 –

9. Try these perfect squares

10. Non-Perfect Squares Why isn’t 20 a perfect square? 20 1 2 4 10 5 Area = 20 Area = 20 Area = 20 The square root of 20 must be a decimal or fraction number between 4 and 5. Nothing times itself equals 20

11. How to find an approximation of the square root of 20… Decimal Form What two perfect squares does 20 lie between? 16 and 25 The square root of 16 is 4, so the square root of 20 must be a little more than 4. How to find the “little more” Is the “non-perfect square” 20 closer to 16 or 25? It seems to be right in the middle. So pick a number in between 4 and 5. Multiply 4.4 times 4.4. What do you get? 19.36 20 – 19.36 = 0.64 Lets see if we can get closer to 20. Multiply 4.5 times 4.5. What do you get? 20.25 20 – 20.25 = -0.25 4.5 is the best estimate for the square root of 20 .

12. How to find an approximation of the square root of 20… Radical Form You can keep your answer in radical form too: Look at the value in the radical √20 Is there a perfect square inside the radical? √2*2*5 Pull out the perfect square and place the number being squared in front of the radical sign...then keep the remaining value inside the radical 2 √5 5 2

13. Example 1: The square root is between two integers. Name the integers & explain. √55 Think: What are perfect squares close to 55? 49 < 55 64 > 55 7 2 = 49 8 2 = 64 √55 is between 7 and 8 because 55 is between 49 and 64. 7.4²=54.76 closest value 7.5²=56.25 keep as √55 since the factors are only 5 * 11 (no perfect square to pull out) OR

14. Example 2: The square root is between two integers. Name the integers & explain. √80 Think: What are perfect squares close to 80? 61 < 80 81 > 80 8 2 = 64 9 2 = 81 √80 is between 8 and 9 because 80 is between 64 and 81. 8.9 ²=79.21 closest value 9.0²=81 write as 4 √5 since the factors are 16 * 5 (16 is a perfect square to pull out) OR

15. Example 3: The square root is between two integers. Name the integers & explain. √45 Think: What are perfect squares close to 45? 36 < 45 49 > 45 (6) 2 = 36 (7) 2 = 49 √45 is between 6 and 7 because 45 is between 36 and 49. 6.7 ²=44.89 closest value 6.8²=46.24 write as 3 √5 since the factors are 9 * 5 (9 is a perfect square to pull out ) OR

16. Perfect Cubes Perfect are cubes of Natural numbers Cubes They LITERALLY describe the 3 3 3 3 3   = 27 3

17. Perfect Cubes           MEMORIZE THEM 1 64 8 125 27

18. CUBE ROOTS   Taking the Cube root of a perfect cube will give you the dimension of one edge of the cube 3 3   = 3 3 3 27

19. Cube Roots UNDO Cubes     INVERSE OPERATIONS     We can use this inverse operation to solve equations with exponents.                    

20.         s = 5m           125

21.   Finding Roots of Fractions . Think: What number squared equals a. Think: What number cubed equals b. You can also separate the radical to make two separate problems  

22. Solve each equation. Practice = – 6 (–6)(–6)(–6) = 36(–6) = –216 1.   2. 3. 4.       2.25

23. Order the following values from least to greatest Which value is BEST represented by the circle

24. Review Slide Estimate a Square Root to Decimal Simplify a Square Root in Radical Form Simplify the Cube Root of a Fraction ⎷39 ⎷40 ⎷ 3 1 125 All Answers are in the Video