The method seems long, but is easy when you get used to it.

Example square root of 6,558,721

Divide the number up in bits of two starting from the right so we then have

6,55,87,21

Take the first bit on the left, in this case 6 and find the highest square of a number that will go into 6. Even if this was a double number it could not be higher than 99 so the highest square you have to consider is 9 squared = 81

answer 2...........2 squared is 4

Show as follows, take the 4 from the 6 = 2, bring down the next pair and also write the 2 on the top.

.......2

2.....6, 55, 87, 21

......4

.......255

Double the 2, gives us 4. But think of it as 40 something.

......2

2.....6, 55, 87, 21

......4

4*....255

Now find the largest number that can replace the * with the full number being multiplied by * with the answer being less than 255

43 times 3 = 129

44 times 4 = 176

45 times 5 = 225

46 times 6 = 276

So it is 5. Make the 4* into 45 and also put the 5 up on the top

.......2 5

2.....6, 55, 87, 21

......4

45....255

.......225

......... 3087

As above, deduct 225 from 255 and then bring down the next pair of numbers

Now we have 25 on the top line. Double it makes 50. Add a * as before to give 50*

So now we have a number of 500 and something up to 509.

Do the same as before 501 times 1, 502 time 2 etc

Looks like maybe 506 times 6

That equals 3036. Looks good. 507 times 7 would be 3549, too big.

We now have

.......2 5 6 With that new 6 added to the top line

2.....6, 55, 87, 21

.....4

45....255

.......225

506....3087

........ 3036

We now do the sum of 3087 minus 3036 and bring down the next pair.

......2 5 6

2.....6, 55, 87, 21

.......4

45...255

......225

506....3087

.........3036

.............5121

On the top line we now have 256. Double it and use it as before with the * at the end

.......2 5 6

2......6, 55, 87, 21

........4

45.....255

.........225

506......3087

...........3036

512*.........5121

This one looks easy 5021 times 1 = 5021. So put in the 1. We now have

.......2 5 6 1 With that 1 added to the top line

2..... 6, 55, 87, 21

........4

45 .....255

.........225

506.......3087

.............3036

5121.........5121

.................5121

0

At the top we have 2561. Try your calculator. We have the correct answer.

I used as an example a number that would give a whole number answer. If the answer was not a whole number, you could just keep going after the decimal point as far as you want.

The last time I had to do this must have been about 50 years ago. It is surprising what one can remember.

Please excuse all the ..........

Seems Yahoo does not like leading spaces. Plus I tried to put underlines in the relevant places and that did not work.