square root of 200
The square root of 200 is approximately 14.1421356237.
To find the square root of 200, follow these steps:
Step 1: Make an estimate
Approximate the square root of 200 to the nearest whole number. In this case, the square root of 200 is between 14 and 15.
Step 2: Choose a starting value
Select a value that is close to the estimate you made. Let's start with 14.
Step 3: Divide the number by the starting value
Divide 200 by 14: 200 ÷ 14 = 14.2857 (rounded to 4 decimal places)
Step 4: Average the result
Find the average of the starting value and the result from Step 3:
(14 + 14.2857) ÷ 2 = 14.14285 (rounded to 5 decimal places)
Step 5: Repeat steps 3 and 4
Continue this process, using the average from Step 4 as your new starting value, until you reach a desired level of accuracy.
14.2857 ÷ 14.14285 = 14.16011
(14.14285 + 14.16011) ÷ 2 = 14.15148
And so on...
Step 6: When to stop
Continue this process until you reach the desired level of accuracy. You can stop when the decimal places no longer change significantly.
Using a calculator, the square root of 200 is approximately 14.14214 (rounded to 5 decimal places).
To find the square root of 200, you have two main options: using a calculator or using manual computation.
Option 1: Using a Calculator
Using a calculator is the quickest and most convenient way to find the square root of 200. Simply input the number 200 into your calculator and then press the square root (√) button. The result should be approximately 14.142136.
Option 2: Manual Computation
If you prefer to manually compute the square root, here's a step-by-step process using the long division method:
1. Start by estimating the square root. In this case, the square root of 200 is between 10 and 15. Let's start with 10.
2. Divide 200 by 10, which gives you 20.
3. Take the average of the result from step 2 (20) and the divisor from step 1 (10), which is 15. This is your next estimate.
4. Divide 200 by 15, which gives you approximately 13.333.
5. Repeat steps 3 and 4 until you reach the desired level of accuracy. Keep refining your estimate until you achieve the desired number of decimal places.
Continuing this process, you will find that the square root of 200 is approximately 14.142136, which is the same result obtained using a calculator.
Note: Remember that the square root of a positive number will have both a positive and negative solution. However, when discussing the square root of a positive number, it usually refers to the positive square root.