What is the approximate value of $?$ in the equation below?

$$199.99 + 12.01\% ext{ of } 499.99 - \sqrt[3]{63.99} = ?^2$$

(Note: You are not required to calculate the exact value, only an approximate one.)

Question

What is the approximate value of $?$ in the equation below?

$$199.99 + 12.01\% 	ext{ of } 499.99 - \sqrt[3]{63.99} = ?^2$$

(Note: You are not required to calculate the exact value, only an approximate one.)

Accepted Answer

**Solution:**

1. Approximate each term:
   - $199.99 \approx 200$
   - $12.01\%$ of $499.99 \approx 12\%$ of $500 = \frac{12}{100} 	imes 500 = 60$
   - Cube root of $63.99 \approx \sqrt[3]{64} = 4$

2. Substitute these approximations into the expression:
   $$200 + 60 - 4 = 256$$

3. The equation is:
   $$256 = ?^2$$

4. Find $?$ by taking the square root:
   $$? = \sqrt{256} = 16$$

**Answer:** $16$

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