Square roots

Posted on 2011-05-03
Last Modified: 2012-05-11
Can someone help me understand the sentence highlighted in blue. What is the root number? Thanks.

Are they referring to a tiny number that sometimes appears at the top just left of the radical sign? And if there is no number their it defaults to 2?
Question by:kadin
    LVL 31

    Accepted Solution

    >> What is the root number?
    >> Are they referring to a tiny number that sometimes appears at the top just left of the radical sign? And if there is no root number, then it defaults to 2?

    LVL 31

    Expert Comment

    Notice that the root number, if not present, is, as you mentioned, 2.

    sqrt( y ) = y^(1/2)

    So sqrt( y^2 ) = ( y^2 )^(1/2)

    There is a rule:   (a^m) ^ n = a ^(mn)  when a > 0
         Careful: In general, this is not the same as  a^(m ^ n)

    So, (a^m) ^ (1/n) = a ^( m*(1/n) ) = a^( m/n )
    and if m = n, then (a^n) ^ (1/n) = a^(n/n) = a^1 = a

    But if a < 0, and if n is even, then if y < 0, we want the n-th root of y^n to be positive. So, to be safe, the absolute value signs are used to handle y either postive or negative.
    LVL 26

    Expert Comment

    "The reason we use the absolute value is ...."          wrong      if the number is even

    If a number is raised to an even power the result is always > 0

    Author Closing Comment

    Thanks to both of you for your help.
    LVL 26

    Expert Comment

    actually I guess they are right if you define simplify in a certain way, which is probably what they are doing

    Author Comment

    phoffric sent me this site link a couple of weeks ago. I am finding it helpful.

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