Find the Domain square root of 49w^16

Problem

√(,49*w16)

Solution

1. Identify the condition for the domain of a square root function. For the expression to be defined in the set of real numbers, the radicand must be greater than or equal to zero.

49*w16≥0

2. Analyze the components of the radicand. The constant 49 is a positive number.

49>0

3. Evaluate the variable term w16 Since the exponent 16 is an even integer, any real number w raised to this power will result in a value that is greater than or equal to zero.

w16≥0

4. Conclude that the product of two non-negative values is always non-negative. Therefore, the inequality 49*w16≥0 holds true for all real values of w

w∈(−∞,∞)

Final Answer

Domain of √(,49*w16)=(−∞,∞)

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