find the square root to the nearest tenth of 13
From Google calculator:
square root(13) = 3.60555128 = 3.6
To find the square root of 13 to the nearest tenth, you can use a calculator or follow these steps manually:
1. Start with an initial guess, such as 3.
2. Divide 13 by the guess: 13 ÷ 3 = 4.3333.
3. Average the guess and the result: (3 + 4.3333) ÷ 2 = 3.6667.
4. Repeat steps 2 and 3, using the new guess:
- Divide 13 by 3.6667: 13 ÷ 3.6667 = 3.5486.
- Average the guess and the result: (3.6667 + 3.5486) ÷ 2 = 3.6076.
5. Repeat these steps, continuing to refine the guess, until you reach the desired level of accuracy.
After following these steps a few more times, you'll find that the square root of 13 to the nearest tenth is approximately 3.6.
To find the square root of 13 to the nearest tenth, you can use a calculator or a mathematical technique called "estimation" by hand. I will explain both methods:
Method 1: Using a calculator
- Enter the number 13 into your calculator.
- Press the square root (√) button.
- The result will be the square root of 13, which is approximately 3.6055512755.
- To round it to the nearest tenth, consider the digit in the hundredth's place. In this case, it is 0. So, we keep the decimal digit in the tenths place as it is and ignore the digits after it.
- Therefore, the square root of 13, rounded to the nearest tenth, is approximately 3.6.
Method 2: Estimation by hand
- Start by guessing a number whose square is close to 13. In this case, you can choose 3, as 3^2 = 9, which is close to 13.
- Divide 13 by your guess (3): 13 ÷ 3 = 4.333333...
- Now, average your guess (3) with the result you obtained (4.333333...): (3 + 4.333333...) / 2 = 3.666666...
- Repeat this process a few more times, taking the average of the previous result and dividing 13 by it, until you reach the desired level of accuracy or precision.
- Continuing this process, you will find that the square root of 13 is approximately 3.6055512755.
- Now, round this value to the nearest tenth by considering the digit in the hundredth's place. Since it is 0, we keep the decimal digit in the tenths place as it is and ignore the digits after it.
- Therefore, the square root of 13, rounded to the nearest tenth, is approximately 3.6.
Both methods should give you the same result: the square root of 13, rounded to the nearest tenth, is approximately 3.6.