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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:
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: 10/3.1667 = 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.
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