How do I do square roots when you have the numbers 42 and 84? This is the best way I could explain it. Hope you know what I'm talking about.
In my case, I use a hand calculator. Before they existed, I used a log table or a slide rule. There is a pencil-and-paper way to calculate square roots that are not integers, but it is rather complicated. Almost no one teaches it anymore. If that is what you want, I may be able to find you a reference.
In the meantime: sqrt(42) = 6.481..
sqrt(84) = 9.165..
I would love you to teach me the method because i am not sure if state tests will ask for that.
There is an example of the method us "oldtimers" had to learn as students, and which I taught to my students before calculators were available.
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
Go about one page down on the site to where it says
"Finding a square root using an algorithm"
and see if you can follow their example.
To attempt to explain it here and show it here is a bit too complicated.
Here is another example using a larger number.
The nice thing about this method is that it gives you the exact decimals up to your point of progress in the solution.
Also it will work for the calculation of square roots of decimals, but you have to start the initial pairing of digits from the decimal point, pairing them going to both the left and the right of the decimal
http://www.homeschoolmath.net/teaching/square-root-algorithm-example.php
To calculate square roots, you can use either a calculator or perform the calculation manually. Let's go through both methods using the numbers 42 and 84 as examples.
1. Using a calculator:
- If you have a scientific calculator, look for the √ or sqrt button.
- Enter the number you want to find the square root of. For example, to find the square root of 42, enter "42".
- Press the √ or sqrt button. The calculator will display the square root of the entered number. In this case, the square root of 42 is approximately 6.481.
- To find the square root of 84, repeat the process by entering "84" and pressing the √ or sqrt button. The calculator will give you the square root, which is about 9.165.
2. Manual calculation:
- To compute square roots manually, we can use a method called "estimation by successive approximations" or utilize mathematical techniques such as the Babylonian method.
- For example, to find the square root of 42, start by taking an initial guess. Let's say we guess that the square root lies between 6 and 7.
- Square the guess: 6 x 6 = 36. Notice that 36 is less than 42.
- Next, increment the guess by a small value. Let's try 0.1, so the new guess is 6.1.
- Square the new guess: 6.1 x 6.1 ≈ 37.21. Now we can see that 37.21 is closer to 42 than 36.
- Repeat this process, incrementing the guess each time, until you reach a value that is very close to the actual square root. In this case, you will approximate the square root of 42 to be 6.48074 (rounded to 5 decimal places).
- For the number 84, you would repeat the same steps and eventually approximate the square root to be 9.16515 (rounded to 5 decimal places).
Remember, using a calculator is more accurate and convenient than manual calculation. However, understanding the manual calculation method can be useful in some scenarios when a calculator is not available.