estimate the square root of 154 to the nearest hundredth

12.41

To estimate the square root of 154 to the nearest hundredth, we can use a calculator or follow the steps manually.

1. Start by finding the perfect squares closest to 154:
- The perfect square less than 154 is 12^2 = 144.
- The perfect square greater than 154 is 13^2 = 169.

2. Take the square root of the closer perfect square:
- √144 = 12

3. Determine the distance between the target number (154) and the closest perfect square (144):
- 154 - 144 = 10

4. Divide the distance by twice the square root of the closest perfect square:
- 10 / (2 * 12) = 10 / 24 = 0.4166... (rounded to the nearest thousandth)

5. Subtract the result from step 4 from the square root found in step 2:
- 12 - 0.4166... = 11.5833...

Therefore, the estimated square root of 154 to the nearest hundredth is approximately 11.58.

To estimate the square root of 154 to the nearest hundredth, we can use the following method:

1. Start by finding two perfect square numbers between which 154 falls. In this case, we can use 12^2 = 144 and 13^2 = 169. So, 154 falls between these two numbers.

2. Take the square root of the smaller perfect square, which is 12. This will be our initial estimate.

3. Next, calculate the difference between the given number (154) and the square of our initial estimate (12^2 = 144). In this case, the difference is 154 - 144 = 10.

4. Divide the difference (10) by twice the initial estimate (2 * 12 = 24). This gives us 10 / 24 = 0.4167.

5. Finally, subtract the result from step 4 from the initial estimate to get the estimated square root of 154: 12 - 0.4167 = 11.5833.

Therefore, the estimated square root of 154 to the nearest hundredth is approximately 11.58.