What approximate value will come in place of question mark (?) in the equation below? (You are not expected to calculate the exact value.)

$$\frac{84.01}{?} + 26.03\% ext{ of } 799.97 + \sqrt[4]{16.03} = (5.99)^3$$

Question

What approximate value will come in place of question mark (?) in the equation below? (You are not expected to calculate the exact value.)

$$\frac{84.01}{?} + 26.03\% 	ext{ of } 799.97 + \sqrt[4]{16.03} = (5.99)^3$$

Accepted Answer

**Solution:**

1. Approximate each term in the equation:
   - $26.03\%$ of $799.97 \approx 26\%$ of $800 = \frac{26}{100} 	imes 800 = 208$
   - $\sqrt[4]{16.03} \approx \sqrt[4]{16} = 2$ (since $2^4 = 16$)
   - $(5.99)^3 \approx 6^3 = 216$

2. Substitute these approximations into the equation:
   $$\frac{84.01}{?} + 208 + 2 = 216$$

3. Simplify the right side:
   $$\frac{84.01}{?} + 210 = 216$$

4. Isolate the fraction term:
   $$\frac{84.01}{?} = 216 - 210 = 6$$

5. Solve for $?$:
   $$? = \frac{84.01}{6} \approx 14$$

**Answer:** $14$

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