May 15, 2013
Steps to Find Square Root
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In this lesson we will see the different methods to find the square root of a number.
Steps to find the square root using averaging and continuous divison method
There are many methods to find the square root of a number. The most commonly used are
 Averaging and continuous division method

Long Divison method
Step by Step prcodeure to find the square root using averaging and continuous method:
Step 1: Divide the given value by the nearest square value, in which the square value should be lesser than the given value
Step 2: Take the average for the calculated result and the divisor which is used.
Step 3: Now divide using the given value and the calculated average value.
Step 4: once again take the average for the calculated above result and the divisor.
Step 5: Now square the above calculated value. The squared value should be equal to given value of the problem, if not repeat the steps 3 and 4.
Example
Find the square root of 2265
Solution:
The square root value for 2265 is nearly equal value to the square values between 47 and 48 , because 47^{2} = 2209 and 48 ^{2} = 2304
Step 1: Divide 2265 by 47.
` 2265 / 47` = 48.1914894
Step 2: Take average for 48.1914894 and 47.
`(48.1914894 + 47 )/2` = 47.5957447
Step 3: Divide 2265 by 47.5957447
`2265 / 47.5957447 ` = 47.5882879
Step 4: Take average for the 47.5882879 and 47.5957447
`( 47.5882879 + 47.5957447 )/2` = 47.5920163
Step 5: check the result by taking square for the calculated value.
47.5920163^{2}^{ }= 2265.00002
This value that is approximately equal to the given value of square root `sqrt 2265`
If the value is not equal to the given value then repeat the steps 4 and 5.
Step 5: One value should be added to the above calculated result it is a divisor, that value should be less than the remainder value.
Step 6: If the requested result is not obtained repeat the steps 2, 3, 4 and 5
Steps to find the square root using long divison method
Steps for finding the square root using long division method:
Step 1: Find the square value that are related to the first value or first two values of the given problem. Approximately equal or exactly equal of the given value. That is dividend value for that divisor
Step 2: Multiply the value by the value itself and then subtract the selected value and the multiplied value.
Step 3: Now here add two values to the resulted value . If not add two zeros place a decimal place in quotient
Step 4: Now multiply the resulted value with 2. This is the dividend value for the divisor value
Example : Find the square root of 2265
Solution:
Long division method.
 85581
 6818198231
The above resulted value is approximately equal to the given square root value, So the answer is 47.59201613
Steps to find square root – Practice Problems:
Problem 1:
Solve the square root of 3434
Answer: 58.6003413
Problem 2:
Solve the square root of 5654
Answer: 75.1930848