sqrt 12
The square root of 12 is approximately 3.4641.
To find the square root of 12, follow these steps:
Step 1: Identify the number you want to find the square root of, which is 12 in this case.
Step 2: Take a guess at the square root of 12. Since 12 is between 9 (3^2) and 16 (4^2), a good initial guess could be 3.5.
Step 3: Divide the number you want to find the square root of (12) by your guess (3.5) to get an updated guess. Perform the division: 12 ÷ 3.5 = 3.428571429.
Step 4: Take the average of your guess (3.5) and the updated guess (3.428571429). (3.5 + 3.428571429) ÷ 2 = 3.4642857145.
Step 5: Repeat Step 3 and Step 4 using the updated guess until you get the desired level of accuracy. In this case, you can repeat steps 3 and 4 one or two more times.
Step 3: 12 ÷ 3.428571429 = 3.492063491.
Step 4: (3.4642857145 + 3.492063491) ÷ 2 = 3.478174603.
Step 3: 12 ÷ 3.478174603 = 3.44821259.
Step 4: (3.478174603 + 3.44821259) ÷ 2 = 3.463193597.
Step 6: Continue repeating steps 3 and 4 until you reach the desired level of accuracy. In this example, the square root of 12 is approximately 3.46.
To find the square root of 12, you can use a calculator or manually calculate it using the long division method. However, I'll explain the manual method for you.
1. Start by estimating the square root. In this case, the square root of 12 is between 3 and 4 since 3^2 = 9 and 4^2 = 16.
2. Assume the square root to be x, so you have x = √12.
3. Take x as the divisor and divide 12 by x to get the quotient.
- Divide 12 by 3: 12 ÷ 3 = 4.
4. Average the divisor (x) and the quotient obtained in the previous step.
- Average of 3 and 4: (3 + 4) / 2 = 3.5.
5. Repeat steps 3 and 4 using the new divisor obtained, until you reach the desired level of accuracy.
- Divide 12 by 3.5: 12 ÷ 3.5 = 3.42857.
- Average of 3.5 and 3.42857: (3.5 + 3.42857) / 2 ≈ 3.46429.
Continue repeating steps 3 and 4 until you reach the level of accuracy you desire. The more you repeat the process, the more precise your square root approximation will be. Eventually, you will get a result close to the actual square root of 12, which is approximately 3.464.