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? 01.jpg
>> 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?
Notice that the root number, if not present, is, as you mentioned, 2.
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.
>> 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?
Yes