Find the Domain square root of 25x^6

Problem

√(,25*x6)

Solution

1. Identify the condition for the domain of a square root function. The expression inside the radical (the radicand) must be greater than or equal to zero.

25*x6≥0

2. Analyze the radicand 25*x6 The constant 25 is a positive number.

25>0

3. Evaluate the variable part x6 Since the exponent 6 is an even integer, any real number x raised to the sixth power will result in a non-negative value.

x6≥0

4. Conclude that the product of two non-negative values is always non-negative. Therefore, the inequality 25*x6≥0 is true for all real numbers x

x∈(−∞,∞)

Final Answer

Domain of √(,25*x6)=(−∞,∞)

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