Algebra 1 Ch.8 (Radicals) Review

The Basics

1

Simplify 

√54

3√6

2

Simplify 

√18x⁵

3x²√2x

3

Simplify

2∛32

4∛4

4

Simplify 

20√63
 5√7

12

5

Find the distance between 

(4,6) and (-4,-9)

17

Adding and Subtracting Radicals

1

Add

4√3 + 2√3 + 7√3

13√3

2

Subtract

6√5 - √125

√5

3

Add

√8 + √98 + √72

15√2

4

Simplify

3√28 - 2√63

0

5

Simplify 

7√18 + 2√25 - 3√72

10 + 3√2

Multiplying Radicals

1

Multiply

√5 x √8

2√10

2

Multiply

(6-√5)(6+√5)

31

3

Simplify 

5√3 (√18 - 2√2)

5√6

4

Simplify 

(√2 + √10)²

12 + 4√5

5

Simplify 

(2√3 - 4)²

28 - 16√3

Rationalizing the Denominator

1

6√7
 √3

2√21

2

  2  
√8

 √2 
  2

3

 √4 
√72

√2
 6 

4

     7     
 3 + √2

3 - √2

5

   √5    
5 - √5

√5 + 1
  4

Solving Radical Equations

1

Solve
√(3x +10) = 2

x = -2

2

Solve
√(x + 4) = √(2x - 1)

x = 5

3

Solve
√(5x + 6) - 6 = 13

x = 71

4

Solve
x + 1 = √(5x + 1)

x = 0, 3

5

Solve
√(x + 1) = 5 - x

x = 3