Square Root

Learning Intention/Success Criteria LI: We are learning to use and simplify square roots SC: I can -use integer operations -use square roots -solve multi-step equations -simplify square roots -find square number factors

Example 1: Show that the given number has a perfect square factor 90 90 1 90 2 45 3 30 5 18 6 15 9 10

Poll Show that the given number has a perfect square factor 75 A] 1 75 B] 3 25 C] 5 15 D] Prime

Guided Practice 1 Show that the given number has a perfect square factor 75 1 75 3 25 5 15

Poll Show that the given number has a perfect square factor 200 A] 1 200 B] 2 100 C] 4 50 D] 5 40 E] 8 25 F] 10 20

Guided Practice 2 Show that the given number has a perfect square factor 200 1 200 2 100 4 50 5 40 8 25 10 20

Poll Show that the given number has a perfect square factor 12 A] 1 12 B] 2 6 C] 3 4 D] Prime

Guided Practice 3 Show that the given number has a perfect square factor 12 1 12 2 6 3 4

Example 2: Write an equivalent expression for the following: 𝟐𝟎 𝟐𝟎 = 𝟒•𝟓 = 𝟒 • 𝟓 =𝟐 𝟓

Poll Write an equivalent expression for the following: 𝟗𝟎 A] 𝟑 𝟏𝟎 𝐁] 𝟗 𝟏𝟎 𝐂] 𝟏𝟎 𝟑 𝐃] 𝟏𝟎 𝟗 E] 𝟗𝟎 , it’s simplified

Guided Practice 4 Write an equivalent expression for the following: 𝟗𝟎 = 𝟗•𝟏𝟎 = 𝟗 • 𝟏𝟎 =𝟑 𝟏𝟎

Poll Write an equivalent expression for the following: 𝟕𝟓 A] 5 𝟓 𝐁] 𝟑 𝟓 𝐂] 𝟓 𝟑 𝐃] 𝟕𝟓 ; can’t be simplified

Guided Practice 5 Write an equivalent expression for the following: 𝟕𝟓 = 𝟐𝟓•𝟑 = 𝟐𝟓 • 𝟑 =𝟓 𝟑

Poll Write an equivalent expression for the following: 𝟐𝟎𝟎 A] 5 𝟖 𝐁] 𝟏𝟎 𝟐 𝐂] 𝟐 𝟏𝟎 𝐃] 𝟖 𝟓 𝑬] 𝟐𝟎𝟎 ; it’s simplified

Guided Practice 6 Write an equivalent expression for the following: 𝟐𝟎𝟎 = 𝟏𝟎𝟎•𝟐 = 𝟏𝟎𝟎 • 𝟐 =𝟏𝟎 𝟐

Example 3: Write an equivalent expression for the following: 𝟔𝟎𝟎 𝟐 𝟔𝟎𝟎 𝟐 𝟏𝟎𝟎∙𝟔 𝟐 𝟏𝟎𝟎 ∙ 𝟔 𝟐 𝟏𝟎 𝟔 𝟐 5 6

Guided Practice 7 Write an equivalent expression for the following: 𝟑𝟎𝟎 𝟐 𝟏𝟎𝟎∙𝟑 𝟐 𝟏𝟎𝟎 ∙ 𝟑 𝟐 𝟏𝟎 𝟑 𝟐 5 3

Guided Practice 8 Write an equivalent expression for the following: 𝟒𝟎 𝟖 𝟒∙𝟏𝟎 𝟖 𝟒 ∙ 𝟏𝟎 𝟖 𝟐 𝟏𝟎 𝟖 𝟏𝟎 𝟒

Guided Practice 8 Write an equivalent expression for the following: 𝟐𝟓𝟎 𝟐 𝟐𝟓∙𝟏𝟎 𝟐 𝟐𝟓 ∙ 𝟏𝟎 𝟐 𝟓 𝟏𝟎 𝟐

Guided Practice 9 Write an equivalent expression for the following: 𝟑𝟐 𝟐 𝟏𝟔∙𝟐 𝟐 𝟏𝟔 ∙ 𝟐 𝟐 𝟒 𝟐 𝟐 2 2

Example 4: Solve for x 3x2 – 300 = 0 3x2 – 300 = 0 + 300 + 300 ______________ ___ 3 3x2 = 300 ___ 3 x2 = 100 x =  10 Check Your Work: 3x2 – 300 = 0 3x2 – 300 = 0 3(-10)2 – 300 = 0 3(10)2 – 300 = 0 300 – 300 = 0 300 – 300 = 0 0 = 0 0 = 0

Poll Solve the following equation: x2 – 144 = 0 A] x = 72, - 72 B] x = 12, - 12 C] x = 144, -144 D] x = 0

Guided Practice 9 Solve the following equation: x2 – 144 = 0 Check With Work: x2 – 144 = 0 + 144 + 144 (12)2 – 144 = 0 ______________ 144 – 144 = 0 x2 = 144 0 = 0 x =  12 x2 – 144 = 0 (-12)2 – 144 = 0 144 – 144 = 0 0 = 0

Poll Solve the equation: 5x2 – 20 = 0 A] x = 2, -2 B] x = 4, -4 C] x = 5, -5 D] x = 0

Guided Practice 10 Check With Work: Solve the equation: 5x2 – 20 = 0 5(2)2 – 20 = 0 5(4) – 20 = 0 + 20 + 20 ______________ 20 – 20 = 0 5x2 = 20 ___ 5 ___ 5 0 = 0 5x2 – 20 = 0 5(-2)2 – 20 = 0 x2 = 4 5(4) – 20 = 0 x =  2 20 – 20 = 0 0 = 0

Example 5: Solve for x (x + 5)2 = 24 - 5 - 5 ______________________ x = -5

Guided Practice 11 Solve the equation: (x – 7)2 = 81 x – 7 = ± 9 + 7 ________________ x = 7 ± 9 x = 7 + 9 x = 7 - 9 x = 16 x = - 2

Guided Practice 12 Solve the equation: (x – 8)2 = 50 x – 8 = x – 8 = + 8 ________________ + 8 x =