1. Simplifying Radicals
The Algebra of Solving Equations

2.  Test the radicand (number inside the radical)
for divisibility by numbers that are perfect
squares.
 Rewrite the radicand as a product of a
perfect square and another number.
 Take the square root of the perfect square
and write the result in front of the radical.

3. 20
2
2 4
2
3 9
2
4 16
2
5 25
2
6 36
4 5
2 5

4. 48
2
2 4
2
3 9
2
4 16
2
5 25
2
6 36
16 3
4 3

5. 27
49
2
2 4
2
3 9
2
4 16
2
5 25
2
6 36
9 3
49

3 3
7
27
49

2
7 49

6. 5 2 3 7
5 3 2 7  
15 2 7 
15 14

7. 3 12 2 15
3 4 3 2 15 
3 2 3 2 15 
6 3 2 15
12 45
12 9 5
36 5

8. 13
2
13
2

13
2
2
2

26
4
26
2

9. 21
6
21
6

21
6
6
6

126
36
126
6
9 14
6

3 14
6
14
2

10. 2
81x 
2
81 0x  
  9 9 0x x  
9, 9x  

11. 2
81x 
9, 9x  
2
81x  
9x  

12. 2
40x 
2 10, 2 10x  
2
40x  
2 10x  

13. 2
7 43x  
5 2, 5 2x  
2
50x  
5 2x  
2
50x 

14. 2
4 11 59x  
2 3, 2 3x  
2
12x  
2 3x  
2
4 48x 
2
12x 

15.  
2
7 60x  
7 2 15, 7 2 15x   
 
2
7 60x   
7 2 15x   
7 2 15x  

16. p. 269
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