Square root of 123 rounded to the nearest hundredth
The square root of 123 rounded to the nearest hundredth is approximately 11.09.
To find the square root of 123 rounded to the nearest hundredth, follow these steps:
1. Start with an initial guess. Let's start with the guess of 10.
2. Divide 123 by the guess (10) and get the quotient: 123 / 10 = 12.3.
3. Compute the average of the guess and the quotient: (10 + 12.3) / 2 = 11.15.
4. Repeat steps 2 and 3 until you achieve the desired level of accuracy.
Let's continue this calculation:
5. Divide 123 by the updated guess (11.15) and get the quotient: 123 / 11.15 ≈ 11.04.
6. Compute the average of the guess and the new quotient: (11.15 + 11.04) / 2 ≈ 11.095.
7. Repeat steps 5 and 6 a few more times to refine the approximation:
- Divide 123 by 11.095 ≈ 11.10.
- Average of 11.095 and 11.10 ≈ 11.0975.
- Divide 123 by 11.0975 ≈ 11.097.
- Average of 11.0975 and 11.097 ≈ 11.09725.
8. Continue this process until you have the desired level of accuracy.
After a few more iterations, the square root of 123 is approximately 11.09053 when rounded to the nearest hundredth.
To find the square root of 123, rounded to the nearest hundredth, you can use a calculator.
Here are the steps to find the square root of 123:
1. Turn on your calculator and find the square root (√) function. It is usually represented by a symbol resembling a checkmark or the letters "sqrt".
2. Enter the number 123 into the calculator.
3. Press the square root (√) button to calculate the square root of 123.
4. The result will be displayed on the calculator screen. To round it to the nearest hundredth, look at the two decimal places after the decimal point.
If the number is less than 0.005, you can round down, and if it is 0.005 or greater, you can round up.
For example, if the square root of 123 is approximately 11.09054, when rounded to the nearest hundredth, it becomes 11.09.
So, the square root of 123, rounded to the nearest hundredth, is 11.09.