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Workbook

RADICALS

Definition of Square Root:

2
b
For any real numbers a and b , if a  , then a is a square root of b and a   b .
a
a) The number a , satisfying b  , is called as positive square root of b .
b) The number a , satisfying  b   a , is called as negative square root of b .

9 3 9 3
Example 1: 36  , 6  36   , 6 0   0  , 0  ,   
16 4 16 4

Remark A:

a) 1  R

b) The number is called as perfect square if the square root of itself is a rational number.

9 9 3
5
Example 2: 25 , 0 , 04 , are called as perfect squares because 0,04  0,2 ,  , 25 
16 16 4

 , ifx x  0
Definition: For x R , x 2  x  
  , ifx x 0

( ) 3 2   3  , 3 5  5  , 5
2
Example 3:  ( ) 7 2    7   , 7 (a  ) 2 2  a  , 2

 (x  ) 2 2   x  , 2 x  x  x 2
2
4

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