What will come in place of the question mark (?) in the following questions?

$14\frac{2}{7}\%\text{of}4200÷\sqrt{576}={\left(?\right)}^{\frac{1}{2}}$

The correct option is 625.

Let us solve the given mathematical expression step-by-step to find the value of the question mark (?).

The given equation is:

$14\frac{2}{7}\%\text{of}4200÷\sqrt{576}={\left(?\right)}^{\frac{1}{2}}$

Step 1: Convert the mixed fraction percentage into a simple fraction.
$14\frac{2}{7}\%=\frac{(14\times 7)+2}{7}\%=\frac{100}{7}\%=\frac{100}{7\times 100}=\frac{1}{7}$

Step 2: Simplify the square root term.
$\sqrt{576}=24$

Step 3: Evaluate $14\frac{2}{7}\%\text{of}4200$.
$\frac{1}{7}\times 4200=600$

Step 4: Perform the division on the left side of the equation.
$600÷24=25$

Step 5: Equate the result to the right side of the equation and solve for ?.
$25={\left(?\right)}^{\frac{1}{2}}$

Squaring both sides to eliminate the exponent 1/2 (square root):
${25}^2=?$

$?=625$

Thus, the value of (?) is 625.