Approximate the value of the square root of 8 to the nearest thousandth.
By what method???
I just punched it in my calculator and got
√8 = appr 2.828
or
I knew from "way back when" that √2 = 1.414..
and since √8 = 2√2, I just doubled 1.414 in my head to get 2.828
that was correct thank you!
To approximate the value of the square root of 8 to the nearest thousandth, you can use a calculator or the method of estimation.
Here's one way to estimate the value:
1. Start with an initial guess. In this case, let's start with the guess of 2.
2. Square the guess: 2 * 2 = 4.
3. Compare the result to the original number. 4 is less than 8.
4. Increase the guess slightly. Let's try 2.5 as the next guess.
5. Square the new guess: 2.5 * 2.5 = 6.25.
6. Compare the result to the original number. 6.25 is still less than 8.
7. Repeat steps 4 to 6, gradually increasing the guess, until the squared result is just greater than 8.
- Let's try 3 as the next guess. Square it: 3 * 3 = 9, which is greater than 8.
- Now we know that the square root of 8 is somewhere between 2.5 and 3.
8. To refine the approximation further, you can continue with smaller increments. For now, let's split the difference and try 2.75 as the next guess.
9. Square the new guess: 2.75 * 2.75 = 7.5625.
10. Compare the result to the original number. 7.5625 is still less than 8.
11. Repeat steps 8 to 10, gradually increasing the guess until the squared result is just greater than 8.
- Let's try 2.8 as the next guess. Square it: 2.8 * 2.8 = 7.84, which is greater than 8.
12. Now we know that the square root of 8 is somewhere between 2.75 and 2.8.
13. To refine the approximation further, you can continue with smaller increments. Let's split the difference and try 2.775 as the next guess.
14. Square the new guess: 2.775 * 2.775 = 7.698625.
15. Compare the result to the original number. 7.698625 is still less than 8.
16. Repeat steps 13 to 15, gradually increasing the guess until the squared result is just greater than 8.
- Let's try 2.78 as the next guess. Square it: 2.78 * 2.78 = 7.7284, which is greater than 8.
17. Now we know that the square root of 8 is somewhere between 2.775 and 2.78.
18. To further refine the approximation, you can continue these steps with even smaller increments until you achieve the desired level of accuracy, or you can use a calculator to find the square root of 8.