What approximate value come in the place of ‘x’ in the following questions.

$39.98\%\text{of}249.99+\sqrt{196.04}=x^2+55.93$

To find the approximate value of x, we can round the decimal numbers in the given equation to their nearest convenient integers:

- $39.98\%$ can be rounded to $40\%$
- $249.99$ can be rounded to $250$
- $\sqrt{196.04}$ can be rounded to $\sqrt{196}$, which is equal to $14$
- $55.93$ can be rounded to $56$

Now, substitute these approximated values back into the original equation:

$40\%\text{of}250+14=x^2+56$

First, calculate the percentage term:

$40\%\text{of}250=\frac{40}{100}\times 250=100$

Substitute this value back into the equation:

$100+14=x^2+56$

$114=x^2+56$

Isolate the variable term $x^2$ by subtracting 56 from both sides:

$x^2=114-56$

$x^2=58$

Take the square root of both sides to find x:

$x=\sqrt{58}$

Since $7^2=49$ and $8^2=64$, the value of $\sqrt{58}$ is approximately $7.61$, which is closest to the integer $8$.

Therefore, the approximate value that comes in place of 'x' is 8.