Final answer:
The value of x when x squared equals 60 is the positive or negative square root of 60, which simplifies to ±2±²(15). The approximate decimal values provided (0.0216 and -0.0224) likely contain a typo and should be verified for accuracy.
Step-by-step explanation:
If we are given x2 = 60, to find the value of x, we need to take the square root of both sides of the equation. When taking the square root of a number, there are always two possible solutions in the real number system: one positive and one negative. Therefore, x can be either the positive square root of 60 or the negative square root of 60. Thus, x = ±60 or x = -±60.
To simplify the square root of 60, we factor it into its prime factors. The number 60 can be factored into 2² × 3 × 5. The square root of 2² is 2, so we can take that out of the square root, leaving us with 2±²(3 × 5). Since neither 3 nor 5 is a perfect square, we cannot simplify further, so the final answer is x = ±2±²(15), which can be approximately x = 0.0216 or x = -0.0224 when we consider possible small errors present in the decimals provided.
Now, it's important to evaluate the provided decimals carefully because there might be a typo since the square root values are different to what we would expect from the square root of 60. For precision, it is recommended to only state the exact simplified square roots or the correct decimal approximation.