# Math

posted by .

How do you find out the square root of a decimal?

ex. 2.31

• Math -

You could use a calculator.

• Math -

I need to do it without a calculator

• Math -

This 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

## Similar Questions

1. ### 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 …
2. ### Math Help!

Four students worked to find an estimate for square root 22. Who is closest to finding the true estimate?
3. ### Calculus

A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum?
4. ### Math

simplify the expression (4 square root of x)/(6-square root of x) I need help with this. I've worked it out to the point where i got (2 square root of x)/(3-square root of x), but I'm pretty sure that it can be simplified further. …
5. ### Math

simplify the expression (4 square root of x)/(6-square root of x) I need help with this. I've worked it out to the point where i got (2 square root of x)/(3-square root of x), but I'm pretty sure that it can be simplified further. …
6. ### math

1. Which of the following numbers is a rational?
7. ### Math

1. Which of the following numbers is a rational?
8. ### math

1. Which of the following numbers is a rational?
9. ### Math

1. Which of the following numbers is a rational?