1. Unit 3. Day 16.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Solving equations with a square roots & cube roots
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational

3. Today’s Lesson
1) Using Square Roots to solve equations
2) Using Cube Roots to solve equations

4. Example A: Solve for the variable.
𝑥 2 = 9 𝑥 = 3 3
Let’s check the answer:
𝑥 2 = 9
2 = 9 −3 ?
It works!
9 = 9

5. 𝑛 2 = 49 𝑛 = ± 7 7 2 = 49 −7 Example B: Solve for the variable.
𝑛 2 = 49 𝑛 = 7 7
2 = 49 −7
Let’s check the answer:

6. This always confused me in high school
This always confused me in high school. I had to ask about this all the time! 36
𝑥 2 = 36
𝑥=±6 6

7. Example C: Solve for the variable.
𝑚 2 = 75 𝑚 = 75 3 ∙ 5 ∙ 5 75
± 5 3 3 25 5 5

8. 𝑥 𝑥−3 −51=−3𝑥+13 −51=−3𝑥+13 𝑥 2 −3𝑥 𝑥 2 −51=13 𝑥 2 = 64 𝑥 = ± 8
Example D: Solve for the variable.
𝑥 𝑥−3 −51=−3𝑥+13
−51=−3𝑥+13
𝑥 2
−3𝑥
+3𝑥
+3𝑥
𝑥 2 −51=13
+51
+51
𝑥 2 = 64 𝑥 = 8

9. 𝑇ℎ𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚𝑠 𝑎𝑟𝑒 ′ 𝑐 𝑜𝑛𝑡𝑟𝑖𝑣𝑒 𝑑 ′ 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑜𝑜𝑘 𝐴𝑙𝑔𝑒𝑏𝑟𝑎 1 𝑈ℎ−𝑜ℎ!
Example D: Solve for the variable.
𝑥 𝑥−3 −51=−3𝑥+13
−51=−4𝑥+13
−4𝑥
𝑥 2
−3𝑥
+4𝑥
+4𝑥
𝑥=−𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
𝑥 2 +𝑥−51=13
+51
+51
𝑥 2 +𝑥 = 64
𝑇ℎ𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚𝑠 𝑎𝑟𝑒 ′ 𝑐 𝑜𝑛𝑡𝑟𝑖𝑣𝑒 𝑑 ′ 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑜𝑜𝑘
𝐴𝑙𝑔𝑒𝑏𝑟𝑎 1
𝑈ℎ−𝑜ℎ!

10. Example E: Solve for the variable. [Contrived]
𝑥 2 −14=5𝑥+67−5𝑥
𝑥 2 −14 = 67
+14
+14
𝑥 2 = 81 𝑥 = 9

11. Example F: Solve for the variable.
𝑥 2 −10 =8
+10
+10
𝑥 2 = 18 18 𝑥 = 18 2 ∙ 3 ∙ 3 2 9
± 3 2 3 3

12. Example G: Solve for the variable.
4𝑥 2 −1 =8 +1 +1
4𝑥 2 = 9 4 4
𝑥 2 = 9 4
3 2 𝑥 =

14. Today’s Lesson
1) Using Square Roots to solve equations
2) Using Cube Roots to solve equations

15. ≠ 3 3 𝑥 3 = 8 𝑥 = ± 2 2 3 = 8 −2 Example H: Solve for the variable.
𝑥 3 = 8 𝑥 = 2 2 ≠
3 = 8 −2
Let’s check the answer:

16. Example I: Solve for the variable.3 3
𝑦 3 = −64 𝑥 = − −4 4 4 ≠
3 = −64
3 = −64
Let’s check the answer:

17. Example J: Solve for the variable.
−3𝑥 =−67
−14
−14
−3𝑥 3 = −81 −3 −3 3 3
𝑥 3 = 27 𝑥 = 3

18. Example K: Solve for the variable.
4𝑥 3 =
4 3
𝑥 3 = =
64 𝑥 3 64 64 3 3
𝑥 3 = 27 𝑥 = 3