Find the approximate value of √11

The correct option is 3.34.

To find the approximate value of the square root of 11 ($\sqrt{11}$), we can analyze the perfect squares that lie close to 11.
We know that:
$3^2=9$
$4^2=16$

Since 11 lies between 9 and 16, its square root must lie between 3 and 4:
$3<\sqrt{11}<4$

To find a closer approximation, let's test the square of 3.3:
${3.3}^2=10.89$

Next, let's test the square of 3.32:
${3.32}^2=11.0224$

Now, let's test the square of 3.316:
${3.316}^2\approx 10.9958$

Rounding this value to two decimal places gives approximately 3.32. Looking at the given options:
- 3.34
- 3.934
- 3.0034
- 3.544

The option 3.34 is the closest value matching the calculated approximation of the square root of 11.