Final answer:
To solve the equation x^2 + 11 = 24, subtract 11 from both sides, take the square root of both sides, and remember to consider both the positive and negative roots. The final answers, rounded to the nearest hundredth, are approximately x = 3.61 and x = -3.61.
Step-by-step explanation:
To solve the equation x^2 + 11 = 24 using square roots, we first isolate the x term by subtracting 11 from both sides of the equation, which gives us:
x^2 = 24 - 11
x^2 = 13
Next, we take the square root of both sides to solve for x. Remember, when taking the square root of both sides of an equation, there are always two solutions: a positive and a negative square root. Therefore, we get:
x = ±√13
When rounded to the nearest hundredth, our solutions are: