Thursday

April 2, 2015

April 2, 2015

Posted by **6th grader** on Wednesday, July 29, 2009 at 4:24pm.

ex. 2.31

- Math -
**Ms. Sue**, Wednesday, July 29, 2009 at 4:29pmYou could use a calculator.

- Math -
**6th grader**, Wednesday, July 29, 2009 at 4:35pmI need to do it without a calculator

- Math -
**MathMate**, Wednesday, July 29, 2009 at 4:38pmThis used to be taught to 6th graders back in the 1910's. With the advent of calculators and computers, the method got lost from the system. Some home schooling programmes still do it.

1. By modern calculator

Assuming you have a calculator, press 2.31 followed by the √ key.

2. By simple calculator

If your calculator does not have a √ key, you can do it by trial and error. Try to square 1.5 (=2.25), too small. Try 1.6² (=2.56), too big. So the square root is somewhere in between Keep trying and halving the gap, for example, try 1.55 in this case.

3. By simple calculator using Newton's method.

From a given estimate x, calculate a better estimate using

x1=x + (2.31-x²)/(2x)

Keep repeating the same procedure until the desired accuracy is achieved.

Example:

x=1.5

x1=1.5+(2.31-1.5²)/(2*1.5)=1.52

x2=1.52+(2.31-1.52²)/(2*1.52)=1.519868

which is already accurate to 6 figures after the decimal point.

4. Manual method.

It is rather difficult to describe the method without having an easy way to align numbers in the response. So I will refer you to a web-site that describes the method:

http://www2.qnet.fi/abehr/Achim/Calculators_SquareRoots.html

**Answer this Question**

**Related Questions**

Algebra - Rationalize each expression by building perfect nth root factors for ...

Math Help! - Four students worked to find an estimate for square root 22. Who is...

Math simplifying mixed radicals - Please help me simplify these following mixed ...

math - Use a calculator and systematic trial to approximate each square root to ...

Math ~CHECK MY ANSWER~ - 1) Which of these is a rational number? a. Pi b. Square...

Math Help - the square root of 3 times the square root of 15 also the square ...

Math simplifying mixed radicals - Please help me simplify these following mixed...

Math - Just need some help... Directions: Multiply or raise to the power as ...

Math PLEASE HELP ASAP - -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT ...

math - What does it mean to have the sqaure root of 5 with a 2 in front of it? ...