Calculate Square Root using Long Division Method - Tutorial

Calculate Square Root using Long Division Method


The square root of number is a number which is multiplied by the same number, which as a result gives the original number back. Its symbol is called a radical and it is represented like this: √


Find the square root for 40 using long division method.


Number = 40

To Find,

Square Root of √40 using Long Division Method


In the above example the number for which we have to calculate square root is 40. Here we doing this using long division method.

Step 1:

Find the largest square smaller than 40, that's 36. Subtract the 36 from the 40, which leaves 4, and enter a 6 as the first digit of your quotient.

Step 2:

Take the reminder 4 and 'bring down' the next pair of digits (00 as it happens) to make 400. Before making 4 into 400 add a decimal point to the answer. Then follow the steps to find next digits.

Step 3:

Use the first digit of our quotient 6 but double it (12) and make that ten times bigger (120). Now find 'something'- a single digit, so that one hundred and twenty 'something' times that same 'something' is as large as possible but less than the 400. (i.e)123 times 3 makes 369, so three is the digit we want (124 times 4 would have been too big).

Step 4:

Subtract the 369 from the 400 (31) and 'bring down' the next pair of digits (so we are now aiming for 3100). The digits we have so far in the quotient are 6 and 3. Double 63 and then make it ten times bigger (1260). Use the same technique as before: find one thousand two hundred and sixty 'something', times 'something', that gets as close as possible to 3100 without exceeding it. Our third digit will be 2, 1262 times 2 is 2524, 1263 times 3 would be too large.

Step 5:

Subtract to leave 576, bring down the next pair of digits, double the digits you already have, that's 632, which doubles to make 1264, now look for twelve thousand, six hundred and forty 'something' times 'something' to come as close as possible to 57,600 without exceeding it. That 'something' is 4 (check it), and so we continue until we have as many digits in our answer as we think we need. Finally the result is 6.324

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