Extracting the square root for grade 9.pptx

math grade 9 ppt

1. Grade 9 – Mathematics Quarter I SOLVING QUADRATIC EQUATIONS BY EXTRACTING SQUARE ROOTS

2. Objectives: 1. familiarize numbers that are perfect squares; and 2. solve quadratic equations by extracting square roots.

3. Quadratic Equations that can be written in the form 𝒙 𝟐 = 𝒌 can be solved by applying the following properties: If 𝑘 > 0, then 𝒙 𝟐 = 𝒌 has two real solutions or roots: 𝑥 = ± 𝑘. If 𝑘 = 0, then 𝒙 𝟐 = 𝒌 has two real solutions or roots: 𝑥 = If 𝑘 < 0, then 𝒙 𝟐 = 𝒌 has no solutions or roots: Speaking Mathematically 𝑥 = ± 36 is read as ‘ 𝒙 is equal to the positive or negative square root of 36 ’ 𝑥 − 5 2 is read as “ the square root of the square of the quantity 𝒙 𝒎𝒊𝒏𝒖𝒔 𝟓 ".

4. 𝑥 2 = 49 𝑥 = ± 7 How to extract square roots?  

5. 𝑥 2 = 169 𝑥 = ± 13 How to extract square roots?  

6. 8 = 4 ∙ 2 32 = 16 ∙ 2 54 = 9 ∙ 6 75 = 25 ∙ 3 12 = 4 ∙ 3 40 = 4 ∙ 10 56 = 4 ∙ 14 76 = 4 ∙ 19 18 = 9 ∙ 2 44 = 4 ∙ 11 54 = 9 ∙ 6 80 = 16 ∙ 5 20 = 4 ∙ 5 45 = 9 ∙ 5 60 = 4 ∙ 15 90 = 9 ∙ 10 24 = 4 ∙ 6 48 = 16 ∙ 3 63 = 9 ∙ 7 96 = 16 ∙ 6 27 = 9 ∙ 3 50 = 25 ∙ 2 68 = 4 ∙ 17 98 = 49 ∙ 2 28 = 4 ∙ 7 52 = 4 ∙ 13 72 = 36 ∙ 2 99 = 9 ∙ 11

7. 8 = 4 ∙ 2 54 = 9 ∙ 6 12 = 4 ∙ 3 56 = 4 ∙ 14 18 = 9 ∙ 2 54 = 9 ∙ 6 20 = 4 ∙ 5 60 = 4 ∙ 15 24 = 4 ∙ 6 63 = 9 ∙ 7 27 = 9 ∙ 3 68 = 4 ∙ 17 28 = 4 ∙ 7 72 = 36 ∙ 2 32 = 16 ∙ 2 75 = 25 ∙ 3 40 = 4 ∙ 10 76 = 4 ∙ 19 44 = 4 ∙ 11 80 = 16 ∙ 5 45 = 9 ∙ 5 90 = 9 ∙ 10 48 = 16 ∙ 3 96 = 16 ∙ 6 50 = 25 ∙ 2 98 = 49 ∙ 2 52 = 4 ∙ 13 99 = 9 ∙ 11 𝑥 2 = 75 Get the square root of both sides Factor the perfect squares Get the square root of the perfect square. 𝑥 2 = 75 𝑥 = ± 25 ∙ 3 𝑥 = ± 25 3 𝑥 = ± 5 3

8. 𝟐 𝒙 − 𝟓 𝟐 = 𝟑𝟐 Divide both sides by 2 Get the square root of both sides 𝒙 − 𝟓 𝟐 = 𝟏𝟔 𝒙 − 𝟓 𝟐 = 𝟏𝟔 𝒙 − 𝟓 = ± 𝟒 𝒙 − 𝟓 = −𝟒 𝒙 = −𝟒 + 𝟓 𝒙 = 𝟏 Find the solutions or roots. 𝒙 − 𝟓 = 𝟒 𝒙 = 𝟒 + 𝟓 𝒙 = 𝟗 𝟐 𝒙 − 𝟓 𝟐 = 𝟑𝟐 𝟐

9. 𝟑 𝟒𝒙 − 𝟏 𝟐 − 𝟏 = 𝟏𝟏 Divide both sides by 3 𝟑 𝟒𝒙 − 𝟏 𝟐 = 𝟏𝟐 𝟒𝒙 − 𝟏 𝟐 = 𝟒 𝟒𝒙 − 𝟏 = 𝟐 4 𝒙 = 𝟑 𝟑 𝒙 = 𝟒 𝟒𝒙 − 𝟏 = −𝟐 4 𝒙 = −𝟏 𝒙 = −𝟏 𝟒 Get the square root of both sides Find the solutions or roots. 𝟒𝒙 − 𝟏 𝟐 = 𝟒 𝟒𝒙 − 𝟏 = ± 𝟐 𝟑 𝟒𝒙 − 𝟏 𝟐 = 𝟏𝟐 𝟑

10. 𝟐𝒙 − 𝟑 𝟐 = 𝟏𝟖 Get the square root of both sides 2𝑥 − 3 2 = 18 2𝑥 − 3 2 = ± 9 ∙ 2 2𝑥 − 3 = ± 9 2 2𝑥 − 3 = ±3 2 2𝑥 − 3 = ±3 2 𝟐𝒙 − 𝟑 = 𝟑 𝟐 𝟐𝒙 = 𝟑 + 𝟑 𝟐 𝒙 = 𝟑 + 𝟑 𝟐 𝟐 𝟐𝒙 − 𝟑 = −𝟑 𝟐 𝟐𝒙 = 𝟑 − 𝟑 𝟐 𝒙 = 𝟑 − 𝟑 𝟐 𝟐

11. 𝟐 𝟓𝒙 + 𝟐 𝟐 = 𝟔𝟒 5𝑥 + 2 2 = 32 5𝑥 + 2 2 = ± 16 ∙ 2 2 5𝑥 + 2 = ± 16 5𝑥 + 2 = ±4 2 𝒙 = Divide both sides by 2 5𝑥 + 2 2 = 32 Get the square root of both sides 5𝑥 + 2 = ± 4 2 𝟓𝒙 + 𝟐 = 𝟒 𝟐 𝟓𝒙 + 𝟐 = − 𝟒 𝟐 𝟓𝒙 = −𝟐 + 𝟒 𝟐 𝟓𝒙 = −𝟐 − 𝟒 𝟐 𝒙 = −𝟐 + 𝟒 𝟐 −𝟐 − 𝟒 𝟐 𝟓 𝟓 𝟐 𝟓𝒙 + 𝟐 𝟐 = 𝟔𝟒 𝟐