$\frac{539}{15}\times \frac{383}{48}=?\times {12}^2$
What approximate value should come in place of the question mark (?) in the following questions?

To find the approximate value that should come in place of the question mark (?), let us write down the given equation:

$\frac{539}{15}\times \frac{383}{48}=?\times {12}^2$

Since we need an approximate value, we can round the numbers to their nearest easily divisible values to simplify the calculation:
- $539$ is very close to $540$, and $540$ is perfectly divisible by $15$:
$\frac{539}{15}\approx \frac{540}{15}=36$
- $383$ is very close to $384$, and $384$ is perfectly divisible by $48$ (since $48\times 8=384$):
$\frac{383}{48}\approx \frac{384}{48}=8$

Now, let us substitute these approximate values back into the left-hand side of our equation:
$36\times 8=288$

On the right-hand side of the equation, we have:
$?\times {12}^2=?\times 1404$

Now, equate the simplified left-hand side to the right-hand side:
$288=?\times 144$

Solving for $?$:
$?=\frac{288}{144}=2$

Thus, the approximate value that should come in place of the question mark is 2.