approximate square root to the nearest integer-------- square root of 46
Sq.Rt. of 36 is 6 and Sq.Rt of 49 is 7
so it's nearest to 7
To approximate the square root of 46 to the nearest integer, you can use a calculator or the long division method.
Using a calculator, the square root of 46 is approximately 6.78. Rounding it to the nearest integer, the approximate square root of 46 is 7.
Using the long division method:
1. Start by guessing a number for the square root of 46. Let's guess 6.
2. Divide 46 by the guess (6): 46 ÷ 6 = 7.6667.
3. Take the average of the guess (6) and the result of the division (7.6667): (6 + 7.6667) ÷ 2 = 6.8333.
4. Repeat steps 2 and 3 until you reach a desired level of accuracy.
- Dividing 46 by the guess (6.8333): 46 ÷ 6.8333 = 6.7398.
- Taking the average of the guess (6.8333) and the result of the division (6.7398): (6.8333 + 6.7398) ÷ 2 = 6.7866.
5. Continue this process until you reach the desired level of precision.
- Dividing 46 by the guess (6.7866): 46 ÷ 6.7866 = 6.7795.
- Taking the average of the guess (6.7866) and the result of the division (6.7795): (6.7866 + 6.7795) ÷ 2 = 6.783.
6. Repeat step 5 if necessary or stop when the desired level of precision is reached.
- Dividing 46 by the guess (6.783): 46 ÷ 6.783 = 6.7808.
- Taking the average of the guess (6.783) and the result of the division (6.7808): (6.783 + 6.7808) ÷ 2 = 6.7819.
7. After a few iterations, if you don't need a high level of precision, you can round the result to the nearest integer. In this case, the rounded result is 7.
Therefore, the approximate square root of 46 to the nearest integer is 7.
To approximate the square root of 46 to the nearest integer, you can use a calculator or follow these steps manually:
1. Start by making an initial guess. Since 46 is between 6 squared (36) and 7 squared (49), we can start by guessing that the square root of 46 is somewhere between 6 and 7.
2. Calculate the average of the initial guess and the result obtained from step 1. In this case, the average of 6 and 7 would be 6.5.
3. Square the average obtained in step 2. In this case, 6.5 squared is 42.25.
4. Compare the result obtained in step 3 with the given number (46). Since it is less than 46, we can conclude that the square root of 46 is larger than 6.5.
5. Repeat steps 2-4, but use the new average (6.5) as the new guess. Continue this process until you arrive at an answer with the desired level of accuracy.
Let's apply these steps:
1. Initial guess: √46 is between 6 and 7.
2. Average: (6 + 7) / 2 = 6.5.
3. Square the average: 6.5^2 = 42.25.
4. Comparison: 42.25 < 46 (since it is less).
5. Repeat steps 2-4.
Next iteration:
2. New average: (6.5 + 7) / 2 = 6.75.
3. Square the average: 6.75^2 ≈ 45.56.
4. Comparison: 45.56 < 46 (since it is less).
5. Repeat steps 2-4.
After a few more iterations, you will find that the square root of 46 is approximately 6.78. Rounded to the nearest integer, the final approximation is 7.
Therefore, the approximate square root of 46 to the nearest integer is 7.