USING DISTRIBUTIVE PROPERTY WITH RADICAL EXPRESSION

Expand and simplify :

Problem 1 :

-√2(3 - √2)

Solution :

-√2(3 - √2)

After distribution, we get

= -√2 ⋅ 3 + √2 ⋅ √2

= -3√2 + √(2 ⋅ 2)

= -3√2 + √4

     = -3√2 + 2

Problem 2 :

-√2(4 - √2)

Solution :

-√2(4 - √2)

= -√2 ⋅ 4 + √2 ⋅ √2

= -4√2 + √(2 ⋅ 2)

 = -4√2 + √4

 = -4√2 + 2

Problem 3 :

-√3(1 + √3)

Solution :

-√3(1 + √3)

 = -√3 ⋅ 1 - √3 ⋅ √3

= -√3 - √(3 ⋅ 3)

 = -√3 - √9

 = -√3 - 3

Problem 4 :

-√3(√3 + 2)

Solution :

-√3(√3 + 2)

= -√3 ⋅ √3 -√3 ⋅ 2

= -√(3 ⋅ 3) - 2√3

= -√9 - 2√3

= -3 - 2√3

Problem 5 :

-√5(2 + √5)

Solution :

-√5(2 + √5)

= -√5 ⋅ 2 - √5 ⋅√5

= -2√5 - √(5 ⋅ 5)

= -2√5 - √25

= -2√5 - 5   

Problem 6 :

-(√2 + 3)

Solution :

-(√2 + 3)

= -√2 – 3

Problem 7 :

-√5(√5 - 4)

Solution :

-√5(√5 - 4)

= -√5 ⋅√5 + √5 ⋅ 4

= -√(5 ⋅ 5) + 4√5

= -√25 + 4√5

= -5 + 4√5

Problem 8 :

-(3 - √7)

Solution :

-(3 - √7)

= -3 + √7

Problem 9 :

-√11(2 - √11)

Solution :

-√11(2 - √11)

= -√11 ⋅ 2 + √11 ⋅ √11

= -2√11 + √(11 ⋅ 11)

= -2√11 + √121

= -2√11 + 11

Problem 10 :

-2√2(1 - √2)

Solution :

-2√2(1 - √2)

= -2√2 ⋅ 1 + 2√2 ⋅ √2

= -2√2 + 2√(2 ⋅ 2)

= -2√2 + 2√4

= -2√2 + 2 ⋅ 2

= -2√2 + 4

Problem 11 :

-3√3(5 - √3)

Solution :

-3√3(5 - √3)

= -3√3 ⋅ 5 + 3√3 ⋅√3

= -15√3 + 3√(3 ⋅ 3)

= -15√3 + 3√9

= -15√3 + 3 ⋅ 3

= -15√3 + 9

Problem 12 :

-7√2(√2 + 3)

Solution :

-7√2(√2 + 3)

= -7√2 ⋅ √2 - 7√2 ⋅ 3

= -7√(2 ⋅ 2) – 21 ⋅ √2

= -7√4 - 21√2

= -7 ⋅ 2 - 21√2

= -14 - 21√2