PreAlgebra
posted by mysterychicken .
Also need help with this one
Approximate the square root to the nearest hundreth:
square root of 1100
Thanks!
MC

You can use the same method of interpolation requested by the earlier question.
A higher accuracy required can be obtained by choosing a better initial guess.
In this case, we choose 33 (*33=1089, <1100) and 34 (*34=1156, >1100).
33*33=1089
34*34=1156
sqrt(1100)
=33+(3433)*(11001089)/(11561089)
=33.164
The precise value is 33.166.
More accuracy and less work can be obtained by Newton's method.
First we choose a close estimate, for example, 33*33=1089
Then we improve the estimate by adding a correction, which is obtained by subtracting the square of the estimate from the target, and divide the difference by twice the estimate.
This can be repeated to get still better results.
Startin estimate = 33
33*33=1089
next estimate
33+(11001089)/(2*33)=33.1667
The precise value is 33.1662 
Thanks a million!!
MC 
mc, what is the name of your text? The NCTM almost 17 years ago decided that a calculator based curriculum was the way to go in math education, and these types of problems (and the skills) were decided to be forgone. Somehow, your text has ignored this. Frankly, I don't know of anyone teaching this anymore. I stimulates my curiosity. Apparently, some homeschoolers are still doing it, and preaching mastery.
http://www.homeschoolmath.net/teaching/squarerootalgorithm.php
Thanks for letting me know the text name. 
MC,
Are you supposed to find the square root by manual method similar to a long division? I am curious, because this is the best method to be used if a known precision is required, and the question did ask for a precision of a hundredth.
If was not clear in this question how it should be done. Same as Bob's case, I am not sure if the method is in the curriculum any more. 
rough appr. of √1100 is 30
1100/30 = 36.6666
average of 30 and 36.666 = 33.3333
1100/33.333 = 33
average of 33.333 and 33 is 33.16666
1100/33.1666 = 33.1658
average of 33.1658 and 33.16666 is 33.166
so √1100 to the nearest hundreth is 33.17
I used Newton's Method.
And of course a calculator to do the divisions. Of course this didn't make much sense, why not just use the calculator to find √1100 if I use the calculator anyway.
I can see the point of the above question had they asked for the approximation to the nearest whole number, but to ask for an "approximation" accurate to 2 decimal places sort of defeats the purpose of the approximation concept. 
I'm just doing the problems my homeschooling gives me...i have no clue how outdated it is.
MC 
Glad to see 3 math enthusiasts all agreeing on this one !

MC,
Here's a link to the manual square root method, a process similar to a long division. It is a method worthwhile learning because you can get the answer to a specified accuracy without a calculator.
Here's the link:
http://www.itl.nist.gov/div897/sqg/dads/HTML/squareRoot.html 
Thanks
MC 
You can find many different algorithms here:
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
"The digit by digit method" mentioned by MathMate and Bob is explained here too.
Another method that is mentioned here that can be used without a calculator is the NewtonRaphson method for
1/sqrt(x), as this is free of divisions.
Respond to this Question
Similar Questions

Math
Just need some help... Directions: Multiply or raise to the power as indicated... Then simplify the result. Assume all variables represent positive numbers. 1. 5(square root of 6) times twothirds(square root of 15)= 3 onethird (square … 
Algebra 2
could you walk me thorugh these problems simplfy square root 18  3 times sqaure root of 50 plus 5 times the square root of 80  2 times the square root of 125 I'm having troubles with the square root of 80 all of the other radicals … 
PreAlgebra
How can I solve this problem, I'm stuck on it: Approximate to the nearest hundreth by interpolation 5*square root of 84.4 Thanks MC 
7th grade math Ms. Sue please
2. Shelly sews a blanket that has an area of 170 square feet. It has 30 square blocks, each the same size. What is the approximate length of each side of a block? 
Algebra
Rationalize each expression by building perfect nth root factors for each denominator. Assume all variables represent positive quantities. I don’t understand how to compute these. Also I don’t have the square root sign so I typed … 
College Algebra
I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root … 
College Algebra help please
I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root … 
College Algebra
I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root … 
Math simplifying mixed radicals
Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are supposed … 
college precalculus
simplify: square root (4/3)square root (3/4) A. 2sqaure root(3)/2 square root (3) B. square root (7/12) C. square root (3)/6 D. 2/square root (3) which answer?