RADICALS part 2


Some properties of radicals:

  1. Radicals can be added;   3 4√15 + 4 4√15 =  7 4√15
    notice that the indices (plural for index) and radicands are the same
    and we added the coefficients 3 and 4

    Try the following example:
    5  3√16 + 7  3√2 =  answer
    7√16 + 7√2 =  answer


  2. Radicals can be subtracted  3 4√15  - 5 4√15   = - 2 4√15
    Notice that the indices and radicands are the same
    and we subtracted the coefficients 3 and - 5 which = -2

    Try the following example:
    4  3√16 - 7  3√2 =   answer
    4  3√16 - 7  3√2 =   answer
    -5  3√16 - (-7)  3√2 = answer


  3. Radicals can be multiplied;
    4 3√9  x   3√81 =
    4 3√9    x  3√3(27)  =
    4 3√9  x   3 3√3  =
    12 3√27 =  36
    Notice that the indices are the same and hence you can multiply the 4 and 3 which equals 12. Plus you can multiply the 9 and 3 under the radical sign which equals 27.
    Next you can take the cube root of 27 which is 3 and multiple it by 12 so that your final answer is 36.


    4. 5 4√16  x  2 4√48 =    answer

    4 √24  x   √32 =    answer
    7 3√9  x  6 3√81 =    answer

  4. Radicals can be divided if the indices are the same.  3√16 / 3√8  =   3√2 

    4√18 / 4√9  =  answer
    5√12 / 5√6  =  answer



  5. Radicals can be written with fractional exponents. So 3√8 can be written as 81/3     4√A3  can be written as A3/4

    7√123 = answer
    19√67 = answer

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