Step 1 :Given the quadratic equation \(x^{2}=17\).
Step 2 :The square root property states that if \(x^{2}=a\), then \(x=\sqrt{a}\) or \(x=-\sqrt{a}\). In this case, \(a=17\).
Step 3 :So, we can use this property to solve the equation.
Step 4 :The solutions to the equation are \(x=\sqrt{17}\) and \(x=-\sqrt{17}\).
Step 5 :Solving for \(x\) gives us two solutions: \(x1 = 4.123105625617661\) and \(x2 = -4.123105625617661\).
Step 6 :Final Answer: The solutions to the equation \(x^{2}=17\) are \(x=\boxed{4.123105625617661}\) and \(x=\boxed{-4.123105625617661}\).