By Soo Jin Lee and Jaehong Shin
Last time we learned the concept of perfect squares and squaring roots.(If you are not comforatbe with these notions yet, review the previous section by clicking here.)
Today we will find square roots of numbers that are not perfect squares without calculator.
There are four steps you need to do for this objects.
1.Estimate- first, get as close as you can by finding two perfect square roots your number is between.
2.Divide- divide your number by one of those square roots.
3.Average- take the average of the result of step 2 and the root.
4.Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
Example: Calculate the square root of 10 to 2 decimal places.
1. Find the two perfect square numbers it lies between.
3^2 = 9 and 4^2 = 16, so lies between 3 and 4.
2. Divide 10 by 3.
10/3 = 3.33 (you can round off your answer)
3. Average 3.33 and 3.
(3.33 + 3)/2 = 3.1667
Repeat step 2: 10/2.1667 = 3.1579
Repeat step 3: Average of 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623
Try the answer-----> Is 3.1623 squared equal to 10? 3.1623 * 3.1623 = 10.0001
If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and step 3.
Note : There are a number of ways to calculate square root without calculator.