A surd is an irrational number that includes a radical symbol and cannot be calculated exactly. Surd laws allow for simplifying expressions involving surds through operations like multiplication, division, and exponentiation. Surds can be added or subtracted if they have the same radical term, but expressions involving unlike surds cannot be fully simplified. Examples demonstrate working through surd arithmetic problems step-by-step using surd laws and properties.

1. Surds

2. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.

3. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab

4. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b

5. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a

6. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50

7. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2
5 2

8. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2
5 2
 ii  x3

9. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2
5 2
 ii  x3  x 2  x
x x

10. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2 5
 iii 
5 2 4
 ii  x3  x 2  x
x x

11. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2 5 5
 iii  
5 2 4 2
 ii  x3  x 2  x
x x

12. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2 5 5 20
 iii    iv 
5 2 4 2 9
 ii  x3  x 2  x
x x

13. Surds
A surd is an irrational number. It is any number that includes a radical
symbol, , and cannot be calculated exactly.
Surd Laws
1) a  b  ab
a a
2) 
b b
 a
2
3) a
e.g.  i  50  25  2 5 5 20 2 5
 iii    iv  
5 2 4 2 9 3
 ii  x3  x 2  x
x x

14. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot

15. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2

16. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2

17. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 

18. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6

19. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6
 iii   
2 1 
2 1

20. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6
 iii   
2 1 
2 1 conjugate surds

21. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6
 iii   2 1  
2 1 conjugate surds
 2 1
1

22. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6
 iii   2 1  
2 1 conjugate surds
 2 1
1
 iv   2  2 
2

23. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6
 iii   2 1  
2 1 conjugate surds
 2 1
1
 iv   2  2 
2
 44 22
 64 2

24. Surd Arithmetic
Like surds can be added or subtracted, unlike surds cannot
e.g.  i  4 3  6 2  3  2 2
 3 38 2
 ii   3  2  6  3 
 18  3 3  6 2  6
 iii   2 1  
2 1 conjugate surds
 2 1
1
 iv   2  2 
2
Exercise 2C; 1, 2adgj, 3behkm, 4adgj, 5ace,
6behk, 8, 10beh, 11ac, 12bdfh, 13aceg,
 44 22
14afil, 15bdh, 16ac, 18ce,19*
 64 2