How do you describe how you can estimate the square root of a number that isn't a perfect square without a calculator?
https://www.quora.com/How-do-I-find-the-square-root-of-a-number-which-is-not-a-perfect-square
you can estimate using linear interpolation. For example, if you want the square root of 28, note that 28 is 3/11 of the way from 25(5^2) to 36(6^2).
So, the root will be somewhere near 3/11 of the way from 5 to 6.
3/11 = 0.27, so expect √28 to be about 5.27
In fact, √28 = 5.2915
To estimate the square root of a number that is not a perfect square without using a calculator, you can use the method of approximation through trial and error. Here's a step-by-step process:
1. Start by finding two perfect squares between which the number falls. For example, if the number is 17, find perfect squares such as 16 (4^2) and 25 (5^2) that 17 lies between.
2. Take the square root of the lower perfect square as your initial estimate. For example, the square root of 16 is 4.
3. Divide the given number by your estimate. In this case, divide 17 by 4 to get 4.25.
4. Average your initial estimate with the result from the previous step. Add these two numbers and then divide by 2. In this case, average 4 with 4.25. (4 + 4.25) / 2 = 4.125.
5. Repeat steps 3 and 4 with the new average. Divide the given number (17) by the new average (4.125) to get 4.121212... and continue this process until you reach the desired level of accuracy.
6. With each iteration, the calculated value should approach the actual square root. Repeat steps 3 and 4 multiple times to refine your estimate and increase accuracy.
By following this method, you can estimate the square root of a number that isn't a perfect square without the use of a calculator.