The Correct Answer and Explanation is:
The value of the expression 0.23√2093 is approximately 10.52.
The image displays the mathematical expression 0.23√2093. To solve this, we must evaluate the product of the decimal 0.23 and the square root of the number 2093. The process involves two main steps.
First, we need to calculate the square root of 2093. The square root symbol, √, asks for a number that, when multiplied by itself, equals the number inside the symbol. Since 2093 is not a perfect square, its square root will be an irrational number, meaning it has a non repeating, non terminating decimal expansion. We can estimate its value; for example, we know that 45 × 45 = 2025 and 46 × 46 = 2116. This tells us the square root of 2093 is between 45 and 46. Using a calculator for a more precise value, we find that √2093 is approximately 45.7493. For better accuracy in our final answer, it is best to use this more precise value in the next step.
The second step is to multiply this result by the coefficient 0.23. The expression is 0.23 × √2093, so we perform the calculation: 0.23 × 45.7493. This multiplication yields approximately 10.522339. The final answer is typically rounded to a practical number of decimal places, such as two, for clarity and simplicity, unless the problem specifies otherwise. Rounding our result to two decimal places gives us 10.52.
In summary, the calculation breaks down into finding the square root of the number under the radical sign and then multiplying that value by the coefficient preceding it. This systematic approach ensures an accurate evaluation of the expression.
