Find the Domain r square root of 16.36^2+11.14^2

Problem

r=√(,16.36+11.14)

Solution

1. Identify the expression as a square root function of the form ƒ(x)=√(,g(x))

2. Determine the condition for the domain of a square root, which requires the radicand (the expression inside the root) to be non-negative.

3. Evaluate the radicand 16.36+11.14 Since both terms are squares of real numbers, they are both non-negative.

4. Calculate the sum of the squares:

16.36=267.6496

11.14=124.0996

267.6496+124.0996=391.7492

5. Conclude that since the radicand is a constant positive value (391.7492≥0, the expression is defined. In the context of a constant expression, the domain refers to the set of all possible values for which the expression is defined, which is all real numbers if there were a variable, or simply noting it is a well-defined real number.

Final Answer

r=√(,16.36+11.14)=√(,391.7492)≈19.792655

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