Find the approximate value of the number represented by the question mark (?) in the equation:

$$7364.99 + (5.01)^2 + \sqrt{?} = 7433.11$$

Question

Find the approximate value of the number represented by the question mark (?) in the equation:

$$7364.99 + (5.01)^2 + \sqrt{?} = 7433.11$$

Accepted Answer

**Solution:**

1. Given the equation:
   $$7364.99 + (5.01)^2 + \sqrt{?} = 7433.11$$

2. Calculate the value of $(5.01)^2$:
   - $(5.01)^2 = 5.01 	imes 5.01 = 25.1001 \approx 25.1$

3. Substitute the known values into the equation:
   $$7364.99 + 25.1 + \sqrt{?} = 7433.11$$

4. Add the known terms on the left:
   $$7364.99 + 25.1 = 7390.09$$

5. Now,
   $$7390.09 + \sqrt{?} = 7433.11$$

6. Isolate $\sqrt{?}$:
   $$\sqrt{?} = 7433.11 - 7390.09 = 43.02$$

7. Square both sides to find $?$:
   $$? = (43.02)^2 \approx 43^2 = 1849$$

8. Among the options, $1849$ matches the calculated value.

**Answer:** $1849$

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