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Workbook

For any real numbers a and b , and any positive integer n :

3
b
a) If a  , then a is a cube root of b and b  a
3
n th n
b
a
b) If a  , then a is an n root of b and b 

n
The symbol a is called a radical. Each part of a radical is given a name,
as indicated below. n is called as index, is called as radical sign and

a is called as radicand.

n
Remark B: a) If n is an odd integer, then a  R .

b) If n is an even integer and a  0 then n a  R .

c) If n is an even integer and a0 then n a  R .

3
Example 26:  ,2 5 10 , 7  8  real number.

 ,2 4  ,3 6  9  non – real number.

n
n
Remark: i) If b 0, then b  a  b n a
n
n
ii) b R and n is an odd integer b  a  b n a

Example 27: Write the following radicals in the form .a n b

a) 3 54 b) 80 c) 96
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5

Example 28: Perform the following operations.

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3 27 3  8 3   5 9 4 81
a) b) c) d)

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