What is the approximate square root of 11?

To determine the approximate square root of 11, it is helpful to compare it with perfect squares that are close to 11. The perfect squares nearest to 11 are 9 (which is the square of 3) and 16 (which is the square of 4).

Since 11 is between 9 and 16, we know that the square root of 11 must lie between 3 (the square root of 9) and 4 (the square root of 16). To get a more precise estimate, we can consider values between 3.3 and 3.4.

Calculating the squares of these estimates helps refine our answer:

• Squaring 3.3 gives approximately 10.89, which is slightly less than 11.

• Squaring 3.4 gives approximately 11.56, which is more than 11.

Therefore, since the square of 3.3 is just under 11 and that of 3.4 is above 11, the square root of 11 must be closer to 3.3.

Among the provided options, the value of 3.32 is the closest estimate for the square root of 11, making it the