- #1
Ephratah7
- 69
- 0
What is the easiest way to solve "the square root of 150" etc.. without using calculator?
HallsofIvy said:Perhaps not a simple to calculate but easier to remember:
Choose some "starting" value that is close to the square root. Since 12^{2}= 144 is close to 150, let's start with 12. 150/12= 12.5 (and I didn't use a calculator to do that!) Notice that says 12(12.5)= 150. If x^{2}= 150, x must be between 12 and 12.5. Just because it is easy, let take half way between: 12.25. Now 150/12.25= 12.249 (To 3 decimal places. If you want more accuracy, just keep going- but you are going to wish you could use a calculator!). Again, the square root of 150 must be between 12.25 and 12.49. Halfway between is 12.247. 150/12.247= 12.247 again, to 3 decimal places. Since that is the same as the previous number, the square root of 150, to 3 decimal places, is 12.247.
If you want more accuracy, just keep going.
Those who are aware of Newton's method should recognize that as Newton's method applied to the equation f(x)= x^{2}- 150= 0.
John Creighto said:It sounds like the bisection method to me.
http://en.wikipedia.org/wiki/Bisection_method
gel said:No, bisection is much slower to converge.
John Creighto said:Sorry I saw the above poster taking a midpoint and thought he was using a bisection method. To me the above method is Newton–Raphson method, while from what I learned Newtons method does not look for a mid point as an intermediate step.
TheoMcCloskey said:Hal's "method" is indeed a Newton-Raphson search, for this particular problem of solving
[tex]F(x) = x^2 - A = 0[/tex]
Those who are aware of Newton's method should recognize that as Newton's method applied to the equation f(x)= x^{2}- 150= 0.
1. Start by understanding the problem and identifying what information is given and what is being asked. This will help you determine which math concepts and formulas are relevant to the problem.
2. Use mental math techniques such as rounding, estimation, and breaking down numbers to make calculations easier.
3. Practice basic arithmetic skills, including multiplication tables, division facts, and addition and subtraction with larger numbers.
4. Use visual aids such as drawing diagrams or using number lines to help you visualize and solve the problem.
5. Be patient and don't rush through the problem. Take your time and double check your work to avoid making careless errors.