To square a number is to multiply it by itself. The square root of a number x is a number y such that y2 = x. The square root is the inverse* operation of the square. The square of a square root is the original number. Likewise, the square root of a square is the number you originally squared (except possibly for the sign)	For example: 142 = 196. The square root of 196 is 14. The square of 14 is the square of the square root of 196, which is 196, of course. Likewise the square root of the square of 14, 196, is 14
Note here that the square of a negative number is always positive. This means that any positive number has TWO square roots - a positive one and the negative of that same number. This also means that negative numbers do NOT have normal square roots. Look up imaginary and complex numbers.	The square of 5 is 25. The square of -5 is also 25. The square root of 25 is either 5 OR -5. For this tutorial, we will just do positive roots.

*An inverse operation is one which does the opposite of another operation.

Step 1: Pair off all the digits in the number, both ways from the decimal point. If you have to add zeroes on the right to make a pair, do so, just so all digits to the right of the decimal are in pairs. You don't have to have the first digit paired if it is to the left of the decimal point.	For example: 521.4 should be paired off as 5 21.40
Step 2: Set up the frame and copy the decimal to the top
Step 3: Find the largest whole number whose square is less than the first digit or digit pair. Put this on top.
Step 4: Square it and subtract it from the first digit or digit pair.
Step 5: Bring down the next 2 digits
Step 6: Multiply your entire "dividend" (the number on top) so far by 2, and place to the left of the new set of digits.
Step 7: GUESS how many times this "divisor" will go into the new number (ignore the last digit). If it is close to exact, pick the next number down. Put this guess on top AND IN THE SINGLE BLANK SPACE YOU LEFT.
Step 8: Multiply your guess times the "divisor" and subtract from the new number. If the product was too big, reduce the guess by 1 and try again. If the remainder is bigger than the divisor, you can increase the guess by 1, but remember that the guess is also in the divisor. If the remainder equals the divisor, do not increase the guess.
Step 9: go back to step 5 and repeat until you use up all the pairs. The number on top is the square root to as many places as you tried.

Why does this work?

What if the "divisor" is bigger than the next number to divide into?

What if you have a remainder?

How can you get more digits accuracy?

How can you check your answer?