Find the square root of 196: √196
The square root of 196 is 14.
To find the square root of 196, you can follow these steps:
Step 1: Find the factors of the number 196.
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
Step 2: Determine the perfect square factors.
The perfect square factors of 196 are 1, 4, 49.
Step 3: Take the square root of the perfect square factor(s).
The square root of 1 is 1.
The square root of 4 is 2.
The square root of 49 is 7.
Step 4: Determine all possible square root values.
Since 196 = 14 * 14, the square root of 196 can be written as √(14 * 14).
Step 5: Simplify the expression.
Using the product property of square roots (√(a*b) = √a * √b), we can simplify √(14 * 14) to √14 * √14.
Step 6: Calculate the square root of 14.
The square root of 14 is an irrational number, which we can round to approximately 3.74.
Step 7: Multiply the calculated square root values.
√14 * √14 = 3.74 * 3.74 = 13.888.
Therefore, the square root of 196 (or √196) is approximately 13.888.
To find the square root of 196, √196, we can use the following method:
1. Use a calculator: The simplest way to find the square root of a number is to use a calculator. Many scientific calculators have a square root function, denoted by √ or the "sqrt" button. Simply enter 196 into the calculator and press the square root (√) button to obtain the result.
2. Use a mathematics software or online tool: If you don't have a calculator available, you can use mathematics software or online tools. There are numerous websites and apps that can assist you in calculating the square root of a number. Simply input 196 into the provided space and click the calculate button to find the square root.
3. Manual calculation: If you want to manually calculate the square root, you can use a numerical method such as the Babylonian method. This method involves repeatedly making an approximation and refining it until you obtain a satisfactory result.
Here's how to use the Babylonian method to find the square root of 196 manually:
- Start with an initial guess. Let's start with the guess of 10.
- Divide the number (196) by the guess (10) to get the quotient (19.6).
- Take the average of the guess and the quotient (10 + 19.6)/2 = 14.8. This will be the second guess.
- Repeat the above step, dividing 196 by the new guess and taking the average. Keep repeating until you reach an accurate approximation.
By following these steps with a calculator, you will find that the square root of 196 is exactly 14.
1. 14
2. 25
3. radical symbol (type just the symbol not "radical symbol" in words
4. -5
5. - (subtract symbol)