Lots of people have asked us how to get square roots without a calculator, and lots of others have sent us different ways of doing it!
You'll find the classic method written out for you in Easy Question Evil Answers.
There are other ways of working out square roots on this page. The first methods shown here are probably best for whole numbers, but then there's the proper method for decimals.
At the bottom of this page is how to find square roots by construction!
Method 1 (with no dividing but it's slower)

If you want
361=35
Total number of subtractions = 6 therefore the square root of 36 = 6.

Method 2 (with nasty dividing but it's faster)
 
Method 3 (using a formula)KEITH FROM CANADA sent us this quick method which is usually accurate to about two decimal places. Here's his square root formula: √X = √S + (XS)/2√S X = the number you want the square root of S = the closest square number you know to X
 
Short Cuts!With some numbers you can make life easier for yourself and 75 is one of them.

We're very grateful to Frank La Fontaine from Australia who got in touch and explained the method he'd learnt at school 60 years ago! Of course the great thing about maths is that Frank's method will still work perfectly today. Here is his explanation in his own words  we've presented it here exactly as he sent it to us because we can't see how we'd make it any better!
 
1/ Draw a line the length you want to get the square root of. (e.g. 7 cm) 
2/ Draw an extra bit on the end that is 1 unit long (e.g. add an extra 1 cm) 

3/ Draw a semi circle that sits on your extended line. 
4/ Draw a perpendicular going up to touch the semi circle. The length of this perpendicular is your square root! 

