How do you find the square root of 14 without a calculator?
I know I need to use the square root of 9 which is 3 and the square roots of 16 which is 4. I know the answer is gonna be closer to 4 because 14 is closer to 16. I just can't figure how to get the right answer
you can try trial and error, using closer and closer guesses, or do it by hand.
For example,
3^2 = 9
4^2 = 16
so it is between 3 and 4
3.7^2 = 13.69
3.8^2 = 14.44
so you know it is between 3.7 and 3.8
There are many web sites that explain the method of doing roots manually.
Yes there are many sites but not one of them shows you how to do this, appreciate you trying to help
BS
I can refer you to
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
To find the square root of 14 without a calculator, you can use an iterative method called the "guess and check" method. Here's how you can approach it:
1. Start by making a reasonable initial guess. Based on your observation that 14 is closer to 16 than to 9, a good starting point could be 4.
2. Square your initial guess. In this case, 4^2 equals 16.
3. Compare the squared value with the original number. Here, you can see that 14 is less than 16. So, the actual square root of 14 must be less than 4.
4. From your initial guess, decrease or increase it slightly to get closer to the actual square root. Since you know the answer is less than 4, try using 3.9 as the next guess.
5. Square the new guess, 3.9^2, which is equal to 15.21.
6. Compare the squared value with the original number. Again, you see that 14 is less than 15.21.
7. Repeat steps 4 to 6 by adjusting your guess until you get close enough to the actual square root. For better accuracy, you can continue this trial and error process by adjusting your guess and squaring it until you reach a satisfactory approximation.
Through this iterative process, you will eventually find that the square root of 14 is approximately 3.74. Keep in mind that this is an approximation and the decimal places can be rounded off depending on the level of accuracy required.