1. Approximating Roots Units 1.12 & 1.13

2. Approximating Square Roots: Numbers that are not perfect squares do not have integer square roots. You can use perfect squares to approximate the square root of a number that is not a perfect square. Step 1: Locate the closest perfect squares (one smaller, one bigger). Step 2: Decide which is actually closer to the desired radicand. Example: Estimate. Since 52 is not a perfect square, we need to find two perfect squares that are close to 52. They are: 49 and 64 because or. So, lies between 7 and 8. And since 52 is closer to 49, we know that is closer to 7.

3. Try it! Estimate each square root. Closer to 9 1)

4. Closer to 12 Try it! Estimate each square root. 2)

5. Closer to 10 practice it! Estimate each square root. 3)

6. practice it! Estimate each square root. Closer to -9 4)

7. Get good at it! Estimate each square root. Closer to -14 5)

8. Closer to 5 Get good at it! Estimate each cube root. 6)

9. Closer to 10 Get good at it! Estimate each cube root. 7)

10. Closer to –7 Get good at it! Estimate each cube root. 8)

11. HOMEWORK TIME Approximating Roots 1 WS: 1-21 only

12. LET’S GET CLOSER! Now it’s time to approximate to one decimal place!

13. Approximating Square Roots to one decimal place: Now that we can approximate square roots to between two integers, let’s get a little closer! Step 1: Determine between what two integers the root lies and decide which is closer. Step 2: Make educated guesses to 1 decimal place & try them! Step 3: Decide which is closer! Example: Approximate to one decimal place. Step 1: We know that it lies between 7 and 8 from our previous example—and that it is closer to 7. Step 2: Since it is closer to 7… let’s try 7.2, … What is 7.2 2 ? 7.3 2 ? Which is better?

14. Example: Approximate to one decimal place. Step 1: We know that it lies between 7 and 8 from our previous example—and that it is closer to 7. Step 2: Since it is closer to 7… let’s try 7.1, … What is 7.1 2 ? 7.2 2 ? Which is better? Closer to 7.2 Step 3: Decide which is closer!

15. Try it! Approximate to one decimal place. Closer to 9 9) Closer to 9.3

16. Try it! Approximate to one decimal place. Closer to 12 10) Closer to 11.7

17. Closer to 10 practice it! Approximate to one decimal place. 11) Closer to 10.4

18. Closer to –9 practice it! Approximate to one decimal place. 12) Closer to -8.7

19. Closer to 5 13) Closer to 4.8 New ! Get good at it! Approximate to one decimal place.

20. Closer to –11 14) Closer to -10.9 New ! Get good at it! Approximate to one decimal place.

21. Let’s Get Closer! Now it’s time to approximate to two decimal places!

22. Approximating Roots to two decimal places: Example: Approximate to two decimal places. Step 1: We know that it lies between 7.2 and 7.3 from our previous example—and that it is closer to 7.2. Step 2: Since it is closer to 7.2… let’s try 7.21, 7.22, & 7.23! Closer to 7.21

23. Try it! Approximate to two decimal places. 15) Closer to 9.3 Closer to 9.33

24. Try it! Approximate to two decimal places. 16) Closer to 10.4 Closer to 10.44

25. 17) New ! Closer to 7.75 practice it! Approximate to two decimal places.

26. 18) Closer to -7.44 New ! Get good at it! Approximate to two decimal places.

27. 19) Closer to 8.69 New ! Get good at it! Approximate to two decimal places.

28. HOMEWORK TIME Approximating Roots 2 WS