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How to calculate a square root without a calculator

Practice makes perfect. Practice math at

and should your child learn how to do it

Most people in today's world feel that since calculators can find square roots, that children don't need to learn how to find square roots using any pencil-and-paper method. However, learning at least the "guess and check" method for finding the square root will actually help the students 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, consider letting students learn and practice at least the "guess and check" method. Since it actually deals with the CONCEPT of square root, I would consider it as essential for students to learn.

Depending 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.

Finding square roots by guess & check method

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 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.

Example: what is square root of 20?

You can start out by noting that since √ 16 = 4 and √ 25 = 5, then √ 20 must be between 4 and 5.

Then make a guess for √ 20 ; let's say for example that it is 4.5. Square that, see if the result is over or under 20, and improve your guess based on that. Repeat this process until you have the desired accuracy (amount of decimals). It's that simple and can be a nice experiment for students!

Example: Find √ 6 to 4 decimal places

Since 2 2 = 4 and 3 2 = 9, we know that √ 6 is between 2 and 3. Let's guess (or estimate) that it is 2.5. Squaring that we get 2.5 2 = 6.25. That's too high, so we reduce our estimate a little. Let's try 2.4 next. 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.

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