Determine the approximate value that should replace the question mark (?) in the following expression (you are not required to calculate the exact value).

$\sqrt[3]{729.14}+{11.01}^3+60.24\%\text{of}449.86=?$

Correct Answer: The correct option is 1610.

Step-by-Step Explanation:

We are asked to find the approximate value of the given expression:

$\sqrt[3]{729.14}+{11.01}^3+60.24\%\text{of}449.86=?$

Step 1: Round off the terms to their nearest convenient whole numbers.

$\sqrt[3]{729.14}\approx \sqrt[3]{729}$

${11.01}^3\approx {11}^3$

$60.24\%\approx 60\%$

$449.86\approx 450$

Step 2: Calculate each component of the expression.

1. Cube root of 729:

$\sqrt[3]{729}=9$

(since 9 × 9 × 9 = 729)

2. Cube of 11:

${11}^3=1331$

(since 11 × 11 × 11 = 1331)

3. 60% of 450:

$60\%\text{of}450=\frac{60}{100}\times 450=6\times 45=270$

Step 3: Combine all the calculated values to find the final approximation.

$?\approx 9+1331+270$

$?\approx 1340+270$

$?\approx 1610$

Thus, the approximate value that should replace the question mark (?) is 1610.