Solve and round to 2 decimal places: root of 236.94
The square root of 236.94 is approximately 15.39
To solve the square root of 236.94 and round it to 2 decimal places, follow these steps:
Step 1: Estimate the answer
Find two perfect squares that the number 236.94 falls between. The perfect square closest to 236.94 is 225 (15^2) and the perfect square after it is 256 (16^2).
Step 2: Divide the number into a group of two digits
Starting from the decimal point in 236.94, divide the number into groups of two digits. In this case, it will be 2369 and 4.
Step 3: Find the square root digit by digit
Starting from the left, find the largest square root digit that, when squared, is less than or equal to 2369. In this case, it is 48. So, the first digit of the square root is 4.
Step 4: Bring down the next group of digits
Bring down the next group of digits (4), which gives us 469.
Step 5: Double the current root and append a placeholder
Double the current root (4) and append a placeholder at the end. This gives us 8 with a placeholder.
Step 6: Find the next digit of the square root
Find the largest digit that can be multiplied by 80 (the current root) and the product is less than or equal to 469. In this case, the digit is 5.
Step 7: Repeat the process until desired precision is achieved
Repeat steps 4 to 6 until you get the desired level of precision or until the digits repeat. Continue appending digits to the right of the decimal point.
Using the steps above, we find that the square root of 236.94 is approximately 15.39 rounded to 2 decimal places.
To calculate the square root of a number such as 236.94, you can use a calculator, computer software, or the mathematical function available in programming languages. However, I can explain the general steps to calculate it manually.
1. Start with an initial guess. Since the square root of 236 is approximately 15, you can start with the guess of 15.
2. Use the following iterative formula to improve the guess:
guess = (guess + (number/guess)) / 2
In this case, the number is 236.94.
3. Repeat step 2 until the guess converges to the desired accuracy. You can set a threshold for how close the guess needs to be to stop the iteration. Alternatively, you can repeat a certain number of times.
Let's apply these steps:
1. Start with a guess: guess = 15
2. Calculate the new guess:
guess = (guess + (236.94/guess)) / 2
guess = (15 + (236.94/15)) / 2
guess = (15 + 15.796) / 2
guess = 15.398
3. Repeat until desired accuracy:
After repeating the formula a few more times, the guess converges to approximately 15.39. Depending on the level of accuracy you require, you can continue this process.
If you round the result to 2 decimal places, the square root of 236.94 is approximately 15.39.