Lia's Math – Home page

Radicals: pg. 1, 2, 3, 4, 5, 6, 7

Contents:

pg.1…..Radicals  – about radicals

pg.2…..Radicals – properties (addition, subtraction, multiplication, division)

pg.3…..Radicals – properties  (raising to the power)

pg.4…..Radicals – properties  (radicals conditions to exist in the real numbers world)

pg.5…..Radicals – hand calculation of  square root

pg.6…..Radicals – exercises

pg.7…..Radicals – answers to exercises

 

About radicals

A radical is written as where n is called index and is always equal or larger than 2 ( ),    is called radical sign and m is called radicand ( is read: nth root of m).

 

To find the nth root of a number, we need to find the number that raised to the power n is equal with that number (radicand).

Radicals are exponential expressions that have as exponent a fraction.

A radical can be written as an exponential expression:

[1]  

 

If , by using the expression [13] from Exponential Expressions Presentation,  [1] becomes:  

The general formula for a radical can be written:

[2]         where    

 

Example:  

 

 When the radicand is 0 the radical is equal with 0 no matter what value the index has.

[3] 

 

Example:  

 When the index has the value 2, the radical is read square root of  m.

Note that, when the index is 2, we write the radical without the index.

 

Example:   is read square root of .

 

 When the index of a radical has the value 3, the radical is read cube root of m.

 

Example:   is read cube root of 4.

Radicals: pg. 1, 2, 3, 4, 5, 6, 7