Directions: Select the approximate value that should replace the question mark (?) in the given equation.

${?}^2\times (24.99\%\text{of}479.98+{7.01}^2)=4224.97$

The correct answer is 5.

Step-by-step explanation:

We are given the following approximation equation to solve:

${?}^2\times (24.99\%\text{of}479.98+{7.01}^2)=4224.97$

Step 1: Approximate the individual terms in the equation.
• $24.99\%$ can be approximated to $25\%$ or $\frac{1}{4}$.
• $479.98$ can be approximated to $480$.
• $7.01$ can be approximated to $7$.
• $4224.97$ can be approximated to $4225$.

Step 2: Simplify the expression inside the parentheses.
First, calculate $25\%\text{of}480$:

$25\%\text{of}480=\frac{25}{100}\times 480=\frac{1}{4}\times 480=120$

Next, calculate $7^2$:

$7^2=49$

Now, add these two values together:

$120+49=169$

Step 3: Substitute the simplified value back into the equation.

${?}^2\times 169=4225$

Step 4: Solve for $?$.

${?}^2=\frac{4225}{169}$

${?}^2=25$

Taking the square root of both sides gives:

$?=\sqrt{25}=5$

Hence, the approximate value that should replace the question mark is 5.