Many school books seem to think that since calculators can find square roots, that kids don't need to learn how to find square roots using any pencil-and-paper method. But learning at least the "guess and check" method for finding the square root will actually help the student UNDERSTAND and remember the square root concept itself! So even though your math book may totally dismiss the topic of finding square roots without a calculator, you can consider to let them practice at least the first method presented here. This method, "guess and check", actually works around what the square root is all about, so I would consider exercises with it as essential to help children understand the concept of square root. Depending on the child, it might be good to concentrate on teaching the concept of square root without taking the time for paper-pencil calculations. In this case, you can study the guess and check method with the help of a simple calculator that doesn't calculate square roots but can quickly do the multiplications. Finding square roots by guess & check method One simple way to find a decimal approximation to, say √2 is to make an initial guess, square the guess, and depending how close you got, improve your guess. Since this method involves squaring the guess (multiplying the number times itself), it actually uses the definition of square root, and so can be very helpful in teaching the concept of square root. Example: what is √20 ? Children first learn to find the easy square roots that are whole numbers, but quickly the question arises as to what are the square roots of all these other numbers. You can start out by noting that (dealing here only with the positive roots) since √16 = 4 and √25 = 5, then √20 should be between 4 and 5 somewhere. Then is the time to make a guess, for example 4.5. Square that, and see if the result is over or under 20, and improve your guess based on that. Repeat the process until you have the desired accuracy (amount of decimals). It's that simple and can be a nice experiment for children. Example: Find √6 to 4 decimal places Since 22 = 4 and 32 = 9, we know that √6 is between 2 and 3. Let's just make a guess of it being 2.5. Squaring that we get 2.52 = 6.25. That's too high, so make the guess a little less. Let's try 2.4 next. To find approximation to four decimal places we need to do this till we have five decimal places, and then round the result. Guess Square of guess High/low 2.4 5.76 Too low 2.45 6.0025 Too high but real close 2.449 5.997601 Too low 2.4495 6.00005025 Too high, so between 2.449 and 2.4495 2.4493 5.99907049 Too low 2.4494 5.99956036 Too low, so between 2.4494 and 2.4495 2.44945 5.9998053025 Too low, so between 2.44945 and 2.4495. This is enough since we now know it would be rounded to 2.4495 (and not to 2.4494). Finding square roots using an algorithm There is also an algorithm that resembles the long division algorithm, and was taught in schools in days before calculators. See the example below to learn it. While learning this algorithm may not be necessary in today's world with calculators, working out some examples can be used as an exercise in basic operations for middle school students, and studying the logic behind it can be a good thinking exercise for high school students. Example: Find √645 to one decimal place. First group the numbers under the root in pairs from right to left, leaving either one or two digits on the left (6 in this case). For each pair of numbers you will get one digit in the square root. To start, find a number whose square is less than or equal to the first pair or first number, and write it above the square root line (2).