How can you calculate the square root of 1.8E-5 without a calculator
1.8E-5 = 18E-6
so, sqrt will be
√18 E -3
You can do that by hand, or just do some estimating
4^2 = 16
4.2^2 = 17.64
4.3^2 = 18.49
So, you can see it is between 4.3 and 4.3
To calculate the square root of a number without a calculator, you can use an approximation method such as the Heron's method or the Babylonian method. Here's a step-by-step explanation of using the Babylonian method to find the square root of 1.8E-5:
1. Start by making an initial guess for the square root. Let's start with an initial guess of 0.1.
2. Calculate the square of the initial guess. In this case, square 0.1 to get 0.01.
3. Divide the target value (1.8E-5) by the square of the initial guess. 1.8E-5 divided by 0.01 equals 0.0018.
4. Take the average of the result obtained in step 3 and the initial guess. Calculate (0.1 + 0.0018) / 2 = 0.0509.
5. Repeat steps 2-4 with the new guess until you reach an approximation that is accurate enough. Let's go through one more iteration:
- Square the new guess (0.0509) to get 0.00258981.
- Divide the target value (1.8E-5) by the square of the new guess. 1.8E-5 divided by 0.00258981 equals 0.00695141.
- Take the average of the result obtained in step 5 and the new guess: (0.0509 + 0.00695141) / 2 = 0.0284257.
6. Continue repeating steps 2-4 until you are satisfied with the accuracy of the result. In this case, you can repeat the steps a few more times until you reach a desired level of accuracy.
It's important to note that this method provides an approximation of the square root, and the more iterations you perform, the more accurate the result will be. The approximation can be as accurate as you want by continuing the process for more iterations.