Square root of 12.4 rounded to the nearest hundredth
The square root of 12.4 rounded to the nearest hundredth is approximately 3.51.
To find the square root of 12.4 rounded to the nearest hundredth, follow these steps:
Step 1: Start with the number 12.4.
Step 2: Estimate the square root by finding two perfect squares that 12.4 falls between. In this case, 12.4 falls between 9 and 16, which are the perfect squares of 3 and 4, respectively.
Step 3: Take the average of these two perfect squares: (3 + 4) / 2 = 3.5.
Step 4: Square the average: 3.5 * 3.5 = 12.25.
Step 5: Compare the result to the original number. Since 12.25 is less than 12.4, the square root is less than 3.5.
Step 6: Repeat steps 3-5, but this time use the lower bound perfect square of 3.
- Average: (3 + 3.5) / 2 = 3.25.
- Squaring the average: 3.25 * 3.25 = 10.5625.
Step 7: Compare the new result to the original number. Since 10.5625 is less than 12.4, the square root is still less than 3.25.
Step 8: Repeat steps 3-5 again using the new upper bound perfect square of 3.25.
- Average: (3.25 + 3.5) / 2 = 3.375.
- Squaring the average: 3.375 * 3.375 = 11.390625.
Step 9: Compare the new result to the original number. Since 11.390625 is less than 12.4, the square root is still less than 3.375.
Step 10: Repeat steps 3-5 once more with the updated upper bound of 3.375.
- Average: (3.375 + 3.4) / 2 = 3.3875.
- Squaring the average: 3.3875 * 3.3875 = 11.46108125.
Step 11: Compare the new result to the original number. Since 11.46108125 is less than 12.4, the square root is still less than 3.3875.
Step 12: Repeat steps 3-5 for the final time with the updated upper bound of 3.3875.
- Average: (3.3875 + 3.4) / 2 = 3.39375.
- Squaring the average: 3.39375 * 3.39375 = 11.48717765625.
Step 13: Compare the final result to the original number. Since 11.48717765625 is greater than 12.4, the square root is greater than 3.39375.
Step 14: Considering the upper and lower bounds found, the square root of 12.4 rounded to the nearest hundredth is approximately 3.39.
Therefore, the square root of 12.4 rounded to the nearest hundredth is 3.39.
To find the square root of 12.4, we can use a calculator or a math function in a programming language. However, let me walk you through the steps to calculate it yourself.
Step 1: Start by making an initial estimate for the square root. Since 12 is approximately between 3^2 (which is 9) and 4^2 (which is 16), we can estimate the square root of 12 as approximately 3.4.
Step 2: Square the estimated value from step 1: 3.4 * 3.4 = 11.56.
Step 3: Compare the squared value from step 2 to the original number (12.4). Since 11.56 is less than 12.4, we need a slightly larger estimate.
Step 4: Adjust the estimate by a small increment. Let's say we increase it by 0.1: 3.4 + 0.1 = 3.5.
Step 5: Repeat steps 2-4 until the squared value is very close to the original number.
Let's go through these steps incrementally:
Square of 3.5 = 3.5 * 3.5 = 12.25.
12.25 is less than 12.4, so we need to increase our estimate again.
Square of 3.6 = 3.6 * 3.6 = 12.96.
12.96 is greater than 12.4, so we need to decrease our estimate.
Now, let's go one more decimal place:
Square of 3.55 = 3.55 * 3.55 = 12.6025.
12.6025 is greater than 12.4, so we need to decrease our estimate.
Square of 3.54 = 3.54 * 3.54 = 12.5316.
12.5316 is less than 12.4, so we need to increase our estimate again.
Square of 3.55 = 3.55 * 3.55 = 12.6025.
Now we finally have an estimate where the squared value is very close to 12.4.
Rounded to the nearest hundredth, the square root of 12.4 is approximately 3.55.