Estimate the value that should replace the question mark (?) in the mathematical expression below.

$?\times (20.01\%\text{of}580.01+\sqrt{196.01})={\left(}^{8.99}+17.01\times 3.03$

The correct option is 6.

To find the estimated value of the question mark (?), we can approximate each decimal number in the given expression to its nearest whole number or easy-to-calculate value.

Let us analyze the given mathematical expression:

$?\times (20.01\%\text{of}580.01+\sqrt{196.01})={\left(8.99\right)}^3+17.01\times 3.03$

Step 1: Round off each number to its nearest integer.

• 20.01% ≈ 20%

• 580.01 ≈ 580

• 196.01 ≈ 196

• 8.99 ≈ 9

• 17.01 ≈ 17

• 3.03 ≈ 3

Step 2: Substitute these rounded values into the expression.

$?\times (20\%\text{of}580+\sqrt{196})=9^3+17\times 3$

Step 3: Simplify individual components.

• $20\%\text{of}580=\frac{20}{100}\times 580=116$

• $\sqrt{196}=14$

• $9^3=729$

• $17\times 3=51$

Step 4: Substitute the simplified values back into the equation.

$?\times (116+14)=729+51$

$?\times 130=780$

Step 5: Solve for the question mark (?).

$?=\frac{780}{130}$

$?=6$

Thus, the value that should replace the question mark (?) is approximately 6.