Find the Domain square root of x^2-5

Problem

√(,x2−5)

Solution

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

x2−5≥0

2. Solve the inequality by first finding the roots of the related equation x2−5=0

x2=5

x=±√(,5)

3. Test the intervals created by the roots −√(,5) and √(,5) to determine where the quadratic expression is non-negative.

(−∞,−√(,5)]∪[√(,5),∞)

4. Express the domain in interval notation based on the values of x that satisfy the inequality.

Domain={[x∈ℝ,x≤−√(,5)* or *x≥√(,5)]}

Final Answer

Domain of √(,x2−5)=(−∞,−√(,5)]∪[√(,5),∞)

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