Approximate the square root of 11 by giving the two whole numbers that it lies between

The square root of 9 is 3. The square root of 16 is 4.

To approximate the square root of 11 and determine the two whole numbers that it lies between, we can use a method called the "guess and check" method.

1. Start by making an initial guess. Let's start with the number 3.

2. Square the number 3: 3² = 9.

3. Compare the result with the original number (11). Since 9 is smaller than 11, we know that the square root of 11 is greater than 3.

4. Increase the guess slightly. Let's try 4.

5. Square the number 4: 4² = 16.

6. Compare the result with the original number (11). Since 16 is larger than 11, we know that the square root of 11 is less than 4.

7. Make a new guess that is in between the previous guesses. Let's try 3.5.

8. Square the number 3.5: 3.5² = 12.25.

9. Compare the result with the original number (11). Since 12.25 is larger than 11, we know that the square root of 11 is less than 3.5.

From the above steps, we can conclude that the square root of 11 lies between 3 and 3.5.

To approximate the square root of 11 and find the two whole numbers it lies between, you can use a method called estimation. Follow these steps:

1. Identify the perfect squares (whole numbers whose square roots are also whole numbers) that are closest to 11. In this case, the perfect squares closest to 11 are 9 (which has a square root of 3) and 16 (which has a square root of 4).

2. Note that since 11 is between 9 and 16, the square root of 11 will be between 3 and 4.

Therefore, the two whole numbers the square root of 11 lies between are 3 and 4.