What is a radical?

Question

I am in honors geometry, and we just went over sines, cosines, and tangents, but I just don't get radicals.

Answer 1

 Radicals are sign for indication of Roots.

 

   Roots are opposite of exponents

 

   

    X^ 2 = ?      What is the value of the quantity that is obtained with multiplying X by itself 2 times

 

    2 ^2 = 4         ''''''''''''''''''''''''''''''''''''''''''''''' 2 ---------------------------------------------

 

    3 ^2  = 9  ------------------------------ 3 -------------------------------------------------

 

     Now if we ask what number has to be multiplied by itself twice to yield 4, 9, then we use √4 , √9

 

         reads . square root of 4, and square root of 9

 

 

          √4 = 2         √9 = 3 / square roots are not written, inside the radical is blank

 

        Roots have order. Square root is also called 2nd order root, for short is always referred to as rad 4,

        rad 9.

 

         Roots can have nth order.

 

          ³√ 8 ,  ⁵√32

         

         2nd , and 3rd order are referred to as square and Cube roots.

 

           The reason for that is because square root is the relation between area of a square, and measure

             of its side, and Cube root  is the measure of side of a cube with Volume V, and its side.

 

           The important relationship is

 

          ⁿ√(X^n) = X 

 

            √ 5^2 = 5        ³√ 3^3 = 3       ⁵√2^ 5= 2

 

          To calculate the any order of ^roots of any number.

 

           We first write the number as product of its prime factor:

 

           √25 = √5 . 5 = √5^2 = 5         ³√ 27 = 3√ 3. 3 .3 = ³√3^3 = 3

   

          Numbers like 4,9, 16,25 , 36, 49, 64, 81, 100, .....

 

          Are all perfect square numbers, i.e, , their square roots are integers, rational numbers.

 

          Any numbers between these , i.e. √5 is not a rational number, to evaluate have to use calculator,

         

           and read the approximation value for it. Geometrically corresponds to the measure of side of a

       

           square with area of 5 units.

 

           You will learn more about when you study Pythagoras Theorem.

                                     

      

 

Answer 2

1) Typically an Islamic Fundamentalist

 

2) All joking aside, radicals are nothing more than the "denominator of exponents" of a number or variable.  Let's look at radical of 'x'

 

X^(1/2) = Square root of X

X^(1/3) = Cube root of X

X^(1/n) = nTH root of X

 

X^(m/n)= n_th-root{x^m} =  [ n_th-root{x} ]^m

 

ie 9^(3/2)=sqrt(9^3) = [ sqrt(9) ]^3 = 27