Part 1 :
How to find the square roots of of numbers that are not perfect squares without a calculator


1  Estimate -

  1. First, get as close as you can by finding the two perfect square roots your number is between.

2  Divide -

  1. Divide your number by one of those square roots.

3  Average -

  1. Take the average of the result of step 2 and the root.

4  Repeat -

  1. Reverage the result of step 3 and repeat steps 2 and 3 until you have a number that is accurate enough for you, i.e., to the hundreths place.

Part 2 :
Example: Calculate the square root of 10 to 2 decimal places.


Find the two perfect square numbers it lies between.

Solution:

โˆš9 = 3 and โˆš16= 4

so,

โˆš10 lies between 3 and 4

Step two:

Divide 10 by 3



10
3
 =3.33

1

Step three:

Average 3.33 and 3



 (3.33+3)
2
 =3.1667

Repeat step two:



 10
3.1667
 =3.1579

Step four:

Average 3.1579 and 3.1667.



(3.1579+3.1667)
2
 =3.1623


Step five:

Now, try squaring the answer. Is 3.1623 squared equal to 10?

3.1623 ยท 3.1623 = 10.0001 2

Repeat steps two and three until the estimate is to the 103 place.

Good enough for 7th grade.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.

Footnotes:

1You can round off your answer to the number of significant digits.
2Since we decided that 102 was significant, we can stop the iterations.

File translated from TEX by TTH, version 3.70.
On 6 Feb 2006, 09:19.