kadin
asked on
Square roots
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?
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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?
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"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
If a number is raised to an even power the result is always > 0
ASKER
Thanks to both of you for your help.
actually I guess they are right if you define simplify in a certain way, which is probably what they are doing
ASKER
phoffric sent me this site link a couple of weeks ago. I am finding it helpful.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut4_radical.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut4_radical.htm
Notation:
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.