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How to calculate square roots without a calculator
The square root of a number, n, written
is the number that gives n when multiplied by itself. For example,
because 10 x 10 = 100
Examples
Here are the square roots of all the perfect squares from 1 to 100.
Finding square roots of of numbers that aren't perfect squares without a calculator
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.
Solution:
32 = 9 and 42 = 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: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623
Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001
If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.
Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.
