Final answer:
After calculating and estimating the values on both sides of the question mark, it is clear that 21 is greater than 8 + √3, so the correct symbol to make the statement true is >.
Step-by-step explanation:
To fill in the appropriate ordering symbol (<, >, or =) to make a true statement 18 + 3 ? 8 + √3, let's first calculate the exact values on both sides of the question mark. The left side of the question is straightforward: 18 + 3 equals 21. The right side involves a square root: 8 + √3. Without a calculator, we estimate that √3 is a little more than 1.7 since the square of 1.7 (1.7 × 1.7) equals 2.89, which is close to 3. Using this approximation, 8 + √3 will be slightly more than 9.7 but clearly less than 10.
Now we make the comparison: 21 is definitely greater than something between 9.7 and 10, which means 21 > 8 + √3. Therefore, the appropriate symbol to make the statement true is >.