How to calculate a square root without a calculator
and should your child learn how to do it 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 methodOne 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. |
|