Limiting condition for roots
There is a restrictive condition in mathematics for calculating and working with roots: The content must not be less than zero (at least for the square root).
Roots - limiting condition simply explained
- Most of them are the so-called. The most common square root, as it is based on the inverse of squaring. However, as both positive and negative Counting are always positive as a square, this (square) root does not exist from a negative number.
- Things look different with higher ones root, for example the cubic or third root. There are no restrictive conditions for the content of the root (root term), since (-a) ³ = -a³. So you can definitely draw cubic roots from negative numbers.
- In general terms, the following applies: In the case of straight roots, the root term must not be negative; there is no restriction for odd roots.
Conditions and examples
- In the expression √a, the restricting condition a ≥ 0 applies to a; So √-4 is not defined. at 3√a the variable a may occupy all real numbers. So is for example 3√-8 = -2 because (-2) ³ = 8.
- The case is somewhat more complicated if the term under the root does not consist only of a number, as in the case √ (x + 4). In order to find restrictive conditions here, i.e. the domain of the root term, you have to determine all x-values for which x + 4 ≥ 0. Solve this inequality and get x ≥ -4.
- An example will be considered in detail, namely √ (x²-1). The condition x²-1 ≥ 0 and thus x² ≥ 1 applies here. As you can easily check, there are no fractions for x whose magnitude is less than 1 and the zero itself. You can only use real numbers in the root term for x that are greater than or equal to 1, or Numbers that are less than or equal to -1. Note that negative numbers (e.g. -4) can also be used here.
"Determine the set of definitions of the root term" - this is how it works
If you have a root function, not all x values result in a y value. That …
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