For example, To find SQRT(1400), simplify to SQRT(100)*SQRT(14), which is equal to 10*SQRT(14). Then find the remaining square root with an estimation method. The 'estimate and check' method is a good exercise in estimating, multiplying, and also memorizing perfect squares.Īnother method, more suitable for students in an algebra class, would be to simplify the radical using the accepted method. This is what I also recommended to my daughter, who is now studying square roots in her home school curriculum. I was happy to see that you recommended the 'estimate and check' method. Do you really believe student at the K-7 level will understand how/why this algorithm works? I fully believe students not be given a calculator to use until advanced algebra or pre-calculus, and then only a scientific calculator (not graphing). I vaguely recall learning the square root algorithm in K-12, but frankly, I see no value in this algorithm except as a curiosity. Whose square is less than or equal to the first pair or first number, and write For each pair of numbers you will get one digit in the square root. 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.Įxample: Find √ 645 to one decimal place.įirst group the numbers under the root in pairs from right to left, leavingĮither one or two digits on the left (6 in this case). There is also an algorithm for square roots that resembles the long division algorithm, and it was taught in schools in days before calculators. This is enough iterations since we know now that √ 6 would be rounded to 2.4495 (and not to 2.4494). Too low, so the square root of 6 must be between 2.44945 and 2.4495.

Too low, so the square root of 6 must be between 2.4494 and 2.4495

Too high so the square root of 6 must be between 2.449 and 2.4495. To find the square root of 6 to four decimal places we need to repeat this process until we have five decimals, and then we will round the result. That's too high, so we reduce our estimate a little. Let's guess (or estimate) that it is 2.5. Since 2 2 = 4 and 3 2 = 9, we know that √ 6 is between 2 and 3. It's that simple and can be a nice experiment for students! Repeat this process until you have the desired accuracy (amount of decimals). Square that, see if the result is over or under 20, and improve your guess based on that. Then make a guess for √ 20 let's say for example that it is 4.5. You can start out by noting that since √ 16 = 4 and √ 25 = 5, then √ 20 must be between 4 and 5. Since this method involves squaring the guess (multiplying the number times itself), it uses the actual definition of square root, and so can be very helpful in teaching the concept of square root. To find a decimal approximation to, say √ 2, first make an initial guess, then square the guess, and depending how close you got, improve your guess. Since it actually deals with the CONCEPT of square root, I would consider it as essential for students to learn.ĭepending on the situation and the students, the 'guess and check' method can either be performed with a simple calculator that doesn't have a square root button or with paper & pencil calculations.įinding square roots by guess & check method So even though your math book may totally dismiss the topic of finding square roots without a calculator, consider letting students learn and practice at least the 'guess and check' method.

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