208 square root to nearest hundredth.
To find the square root of 208 to the nearest hundredth, you can follow these steps:
1. Start by estimating the square root of 208. Since 208 is between the perfect squares of 196 (14^2) and 225 (15^2), you can estimate that the square root of 208 lies somewhere between 14 and 15.
2. To get a more accurate estimation, you can calculate the average of 14 and 15. Add them together and divide by 2:
(14 + 15) / 2 = 29 / 2 = 14.5
3. Now you have a better estimate, but it's still not accurate to the nearest hundredth. To refine the estimation further, you can use the Newton's method or a calculator.
4. If you have a scientific calculator, you can simply enter 208 and then press the square root (√) button. The result, rounded to the nearest hundredth, should be 14.42.
Alternatively, you can use the Newton's method to approximate the square root. Here's the process:
- Start with an initial guess, such as the previous estimate of 14.5.
- Use the formula:
new_guess = (old_guess + (208 / old_guess)) / 2
- Iterate this formula a few times, using the previous guess as the "old_guess" value. Each time, the new guess will get closer to the actual square root.
- After a few iterations, you should arrive at an accurate enough approximation, rounded to the nearest hundredth. In this case, the square root of 208 is approximately 14.42.
Both methods yield the same result: √208 ≈ 14.42 to the nearest hundredth.