Lia's Math – Home page

Radicals – about radicals – pg.1/7

Posted in Math Theory by Lia on 06/01/2013

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 {root{n}{m}} where n is called index and is always equal or larger than n >= 2″ title=”n >= 2″/><img src=),  sqrt{{}{.}{}}  is called radical sign and m is called radicand ( {root{n}{m}} 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]   tabular{11}{11}{{root{n}{m} = m^{1/n}}}

 

If m = p^n, by using the expression [13] from Exponential Expressions Presentation,  [1] becomes:  root{n}{m} = root{n}{p^n} =  (p^n)^{1/n} = {p}^{n*{1/n}} = p^{n/n} = p

The general formula for a radical can be written:

[2]  tabular{11}{11}{{root{n}{m} = p}}       where    m = p^n

 

Example:  root{3}{8} = root{3}{2^3} = 2

 

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

[3]  tabular{11}{11}{{{root{n}{0} = 0}}}

 

Example:  {root{5}{0} = 0}

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

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

 

Example:  {sqrt{7}} is read square root of {{}{7}{}}.

 

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

 

Example:  {root{3}{4}} is read cube root of 4.

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

 

 

 

 

 

 

 

 

 

Tagged with: ,

Leave a Reply