Unit 3. Day 16.

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

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

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

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:

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

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

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

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!

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

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

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

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

≠ 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:

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

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

Example K: Solve for the variable. 4𝑥 3 = 1728 4 3 𝑥 3 = 1728 = 1728 64 𝑥 3 64 64 3 3 𝑥 3 = 27 𝑥 = ± 3