>> 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

Solved

Posted on 2011-05-03

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?

01.jpg

6 Comments

>> Are they referring to a tiny number that sometimes appears at the top just left of the radical sign? And if there is no

Yes

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.

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

http://www.wtamu.edu/acade

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