Estimate the value that should replace the question mark (?) in the mathematical statement below:

$\sqrt[3]{2196.903}÷\sqrt{1520.960}\times 3.102+?=143.991$

The correct option is 143.

To estimate the value of the question mark (?), we round off each decimal number in the mathematical statement to its nearest convenient whole number or perfect power.

Step 1: Round off each term in the given equation.

$\sqrt[3]{2196.903}\approx \sqrt[3]{2197}=13$

(Since 13³ = 2197, the cube root of 2196.903 is approximately 13.)

$\sqrt{1520.960}\approx \sqrt{1521}=39$

(Since 39² = 1521, the square root of 1520.960 is approximately 39.)

$3.102\approx 3$

$143.991\approx 144$

Step 2: Substitute the approximated values back into the equation.

The original statement is:
$\sqrt[3]{2196.903}÷\sqrt{1520.960}\times 3.102+?=143.991$

Substituting the rounded values gives:
$13÷39\times 3+?=144$

Step 3: Simplify the expression following the BODMAS/PEMDAS rule.

Perform the division and multiplication operations from left to right:

$\left(\frac{13}{39}\right)\times 3+?=144$

Simplifying the fraction 13/39 gives 1/3:
$\left(\frac{1}{3}\right)\times 3+?=144$

Multiplying (1/3) by 3:
$1+?=144$

Step 4: Solve for the question mark (?).

$?=144-1$

$?=143$

Hence, the estimated value that should replace the question mark is 143.