Why are the values of the variables different when the radicals are both negatives?
I'm in pre-calc 11 and we're learning about radicals right now. I'm confused with the negative radicals. For example, why does 4w/5 - 6(2w)^1/2 have a restriction of w>0, while -(45n^2)^1/2 has a restriction of n<0. Both of them have a negative radical so why is the value of the variable different?
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The first (4w/5) - 6(2w)^(1/2) has a restriction that w>0 because the square root (which is the same as ^1/2 power) is restricted to positive values.
The second -(45n^2)^1/2 does not have a restriction. 45n^2 is always positive no matter what the value of n, so any value of n will always produce a positive number. The value of this expression is always negative, but that is not what you asked.
Neither has a negative radical, they have rational radicals. If the second was (45n^2)^(-1/2) the restriction would be that n could not equal zero. Because ^(-1/2) power is the same as 1/sqrt(n^2) and division by zero is not defined.
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