Surds and Brackets

Starter Simplify each of the following… 3(2x – 5y) – 2(x – 7) 72 7-2 71/2 4x – 15y + 14 2x2 – 5xy – 14x + 35y 49 1/49 √7

Surds and Brackets This lesson we will focus on strengthening our knowledge and understanding of Surds We will look at problems with brackets as well as simplifying You will also have a go at some exam-style questions

Surds and Brackets A single bracket 2(√2 – 5) = 2√2 - 10 √2 - 5 2 2√2 - 5 2 2√2 - 10

Surds and Brackets A single bracket 3(√5 – √2) = 3√5 - 3√2 √5 - √2 3 - 3√2

Surds and Brackets Two separate brackets 3(√3 + 4) + 2(√3 - 5) = 3√3 + 12 + 2√3 - 10 = 5√3 + 2 √3 + 4 √3 - 5 3 3√3 + 12 2 2√3 - 10

Surds and Brackets Two separate brackets 5(√2 + 5) - √2(√2 - 3) = 5√2 + 25 - √4 + 3√2 = 8√2 + 23 √2 + 5 √2 - 3 5 5√2 + 25 - √2 - √4 + 3√2

Surds and Brackets Two separate brackets √5(√2 + 5√3) - 2√2(3√5 - 4√2) = √10 + 5√15 - 6√10 + 8√4 = - 5√10 + 5√15 + 16 √2 + 5√3 3√5 - 4√2 √5 √10 + 5√15 - 2√2 - 6√10 + 8√4

Surds and Brackets √2 - 3 √3 √6 - 3√3 + √2 + √4 - 3√2 Two brackets together (√2 - 3)(√3 + √2)  √6 - 3√3 + √4 - 3√2  √6 - 3√3 + 2 - 3√2 √2 - 3 √3 √6 - 3√3 + √2 + √4 - 3√2

Surds and Brackets 2√5 + √2 10√10 + 5√4 5√2 3√5 + 6√25 + 3√10 Two brackets together (2√5 + √2)(5√2 + 3√5)  10√10 + 5√4 + 6√25 + 3√10  13√10 + 10 + 30  13√10 + 40 2√5 + √2 10√10 + 5√4 5√2 3√5 + 6√25 + 3√10

Surds and Brackets Other surds-based questions Use the value a = √5. Write out and simplify… a) a2 = √5 x √5 = √25 = 5

Surds and Brackets Other surds-based questions Use the value a = √5. Write out and simplify… b) a-2 = 1/a2 = 1/√5 x √5 = 1/5

Surds and Brackets Other surds-based questions Use the value a = √5. Write out and simplify… c) a3 = √5 x √5 x √5 = √25 x √5 = 5√5

Surds and Brackets Other surds-based questions Use the value a = √5. Write out and simplify… d) a√10 = √5 x √10 = √50 = √25 x √2 = 5√2

Plenary 1/b2 1/√5 x √5 1/5

Plenary ( ) ( ) ( ) √3 √5 x √5 x √9 5 √25 x √9 5 15 5 3 1 2 1 2 1 2

Summary We have continued building on our knowledge of surds We have looked at several examples involving brackets We also have seen some examples of ‘exam-style’ questions