2. Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Square Root Example 1:Find Square Roots Example 2:Find Square Roots Example 3:Find Square Roots Example 4:Find Square Roots Example 5:Use Square Roots to Solve an Equation Example 6:Real-World Example Five-Minute Check

3. Main Idea/Vocabulary Find square roots of perfect squares. perfect square square root radical sign

4. NGSSS MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems.

5. Key Concept

6. Example 1 Find Square Roots Find. Answer:9 Find the positive square root of 81; 9 2 = 81.

7. Example 1 CYP A.5 B.10 C.–10 or 10 D.no real square root Find.

8. Example 2 Find Square Roots Find. Find both square roots of 1.44; 1.2 2 = 1.44. Answer:  1.2

9. Example 2 CYP A.  6 B.0.6 C.  0.6 D.  0.06 Find.

10. Example 3 Find Square Roots Find. Answer: Find the negative square root of

11. Example 3 CYP Find. A. B. C. D.no real square root

12. Example 4 Find Square Roots Find. Answer: There is no real square root because no number times itself is equal to –49.

13. Example 4 CYP A.–11 B.11 or –11 C.–1.1 D.no real square root Find.

14. Example 5 Use Square Roots to Solve an Equation ALGEBRA Solve x 2 = 225. x 2 = 225 Write the equation. x= Definition of square root Answer: The equation has two solutions, 15 and –15. x = 15 and –15 Check 15 15 = 225 and (–15)(–15) = 225

15. Example 5 CYP A.20 B.20 and –20 C.40 and –40 D.no real square root ALGEBRA Solve n 2 = 400.

16. Example 6 PUZZLE A square puzzle has an area of 35,721 square millimeters. What is the length of a side of the square?

17. Example 6 s 2 = 35,721 Write the equation. 35,721= 3 3 3 3 3 3 7 7 Find the prime factors. = (3 3 3 7)(3 3 3 7) Regroup into two equal factors. Definition of square root To find, find two equal factors of 35,721.

18. Example 6 Answer: Since distance cannot be negative, the length of each side is 189 millimeters. So, s = 3 3 3 7 or 189.

19. Example 6 CYP A.57 ft B.114 ft C.228 ft D.6,498 ft MAZES A square corn maze has an area of 12,996 square feet. What is the length of a side of the square?

20. A.–9 B.9 C.–9 or 9 D.3 Five Minute Check 1 Find.

21. A.–12 B.12 C.–12 or 12 D.no real square root Find. Five Minute Check 2

22. A.–4 B.4 C.4 or –4 D.–16 Solve q 2 = 16. Five Minute Check 3

23. Five Minute Check 4 Solve. A. B. C. D.

24. A.–6 B.3.6 C.6 D.1,296 Find the positive square root of 36. Five Minute Check 5

25. A.13 B.14 C.15 D.25 The chairs in the multi-purpose room of a school need to be arranged in a square. There are 225 chairs. How many chairs should be in each row? Five Minute Check 6