How does calculator calculate square root

In fact, one of the calculations we use to determine the amortization of a consumer loan with fees in a given time period is strikingly similar to your square root presentation. The calculation must be written by the software engineer for the machine, so it does ultimately reside in the mind of a human being.

If the engineer doesn't know the algorithm, thousands of consumers will bear the consequences. I suggest that memorization is simply another tool in the box. Use it when its appropriate. The last commenter on the page Adrian said that she never learned the squares from 1 to This brings to mind a trick I recently learned for finding squares close to Start with the square of 50, , add times the distance between 50 and the number, and then add the square of the distance of 50 and the number.

In this identity, x is the distance between 50 and the number. If the number is 43 as in my example , x is If the number is 54, x is 4. So if you memorize your squares from 1 to 25, you get the squares of 26 through 75 "for free".

If the idea of memorizing the squares of 1 to 25 seems daunting, it's not. A few weeks ago, before knowing this trick, I knew just up to 13 offhand, with a few others scattered here and there. I drew up a table in Excel listing numbers 1 to 25 side by side with their squares, printed it out and put it on the wall of my cubicle. Even with not quite knowing them all I can find squares from 1 to 75 in under 10 seconds thought process for finding 73 squared offhand: "73 is 23 greater than What's 23 squared again?

An explanation of why this square root algorithm works. Free worksheets for square roots , including a worksheet generator. A geometric view of the square root algorithm. Square roots by Divide-and-Average Explanation and example of the ancient algorithm for approximating square roots. Square Root Algorithms Formulas for a recurrence relation and Newton's iteration that can be used to approximate square roots.

For the mathematically minded. Square Edging A new method of getting the square root of a special group of numbers in an easier way. I vaguely recall learning the square root algorithm in K, but frankly, I see no value in this algorithm except as a curiosity.

And I am not of the "reform" crowd. 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 was happy to see that you recommended the "estimate and check" method. This is what I also recommended to my daughter, who is now studying square roots in her home school curriculum. The "estimate and check" method is a good exercise in estimating, multiplying, and also memorizing perfect squares.

Another method, more suitable for students in an algebra class, would be to simplify the radical using the accepted method. Then find the remaining square root with an estimation method. Then find SQRT 14 by an estimation method. For square roots of perfect squares, no estimation would even be needed. One could even make the task of finding square roots into a computer programming exercise, having students write a program in javascript or some other language to use a systematic numeric method of estimating this square root via a check and guess method.

Or, at the calculus level, the student could write a program that uses a Taylor Polynomial to evaluate a square root. Michael Sakowski Instructor of Mathematics. Howdy, Noticed several of the comments related to using an algorithm to find the square root of a number.

Some comments appeared to say that finding the result with a paper and pen vs calculator is archaic. That may be so.

However, when I was in my freshman year at high school early 70's Herr Quinnell mentioned - as class was getting out - some of the things one can do with math - including finding square roots. So, I asked him how this was done. He showed me the algorithm method on the board. I cannot speak to the value of generally knowing how this is used in other professions. In electronics engineering, finding square root is an integral part of design. We have parts called resistors.

They aid in limiting current in circuits. These parts have wattage ratings. The value of a resistor is measured in "ohms". In a math sense this can be found by dividing volts by amperes.

As a square root example if I know the 10, ohm resistor has a rating of 0. This is found by taking the resistance value - multiplying the wattage rating - and finding the square root. Square root of is This part could withstand 50 volts. My point - I could have calculated the result using 'artificial means'.

Because somebody took the time to show me how to do square root on a chalkboard, I did not need to hunt down a calculator.

By the time I would have found the calculator I've already figured out an answer. Taking the time to show students how things like square root are done has value. They may not actually put this to use later in life - but some just might.

Garth Price, CET. I was just writing another comment and somehow the computer submitted it before I was done.

I must have tapped the wrong key. So let me just finish by saying that the children are new to the world and are exploring it. Calculating square roots longhand would I believe be fascinating for them and a great way to learn about other topics in math. Oh and by the way I didn't have any lessons at all on square roots until high school and then we didn't learn any way of calculating them.

We were taught to factor the number under the radical and extract perfect squares leaving non-perfect squares under the radical. Bye and God Bless Robert Monroe. To make this article more reader friendly, each step comes with illustrations. To begin, let's organize the workspace. We will divide the space into three parts. For example, the number 7, Or in the case of a number with an odd amount of digits such as 19,, we will start with 1 90 As the next step, we need to find the largest integer i whose square is less than or equal to the leftmost number.

In our current example the leftmost number is Now we need to subtract the square of that integer which equals 16 from the leftmost number which equals The result equals 4 and we will write it as shown above. Next, let's move down the next pair in our number which is We write it next to the subtracted value already there which is 4.

Now multiply the number in the top right corner which is also 4 by 2. Time to fill in each blank space with the same integer i. It must be the largest possible integer that allows the product to be less than or equal the number on the left. A number's factors are any set of other numbers that multiply together to make it. Perfect squares, on the other hand, are whole numbers that are the product of other whole numbers.

For instance, 25, 36, and 49 are perfect squares because they are 5 2 , 6 2 , and 7 2 , respectively. Perfect square factors are, as you may have guessed, factors that are also perfect squares. To start finding a square root via prime factorization, first, try to reduce your number into its perfect square factors. We want to find the square root of by hand. To begin, we would divide the number into perfect square factors. Since is a multiple of , we know that it's evenly divisible by 25 - a perfect square.

Quick mental division lets us know that 25 goes into 16 times. Take the square roots of your perfect square factors. Because of this property, we can now take the square roots of our perfect square factors and multiply them together to get our answer. Reduce your answer to simplest terms, if your number doesn't factor perfectly.

In real life, more often than not, the numbers you'll need to find square roots for won't be nice round numbers with obvious perfect square factors like In these cases, it may not be possible to find the exact answer as an integer.

Instead, by finding any perfect square factors that you can, you can find the answer in terms of a smaller, simpler, easier-to-manage square root. To do this, reduce your number to a combination of perfect square factors and non-perfect square factors, then simplify. However, it is the product of one perfect square and another number - 49 and 3.

Estimate, if necessary. With your square root in simplest terms, it's usually fairly easy to get a rough estimate of a numerical answer by guessing the value of any remaining square roots and multiplying through. One way to guide your estimates is to find the perfect squares on either side of the number in your square root. You'll know that the decimal value of the number in your square root is somewhere between these two numbers, so you'll be able to guess in between them.

Let's return to our example. We'll estimate 1. This works for larger numbers as well. For example, Sqrt 35 can be estimated to be between 5 and 6 probably very close to 6. Since 35 is just one away from 36, we can say with confidence that its square root is just lower than 6.

Checking with a calculator gives us an answer of about 5. Reduce your number to its lowest common factors as a first step.

Finding perfect square factors isn't necessary if you can easily determine a number's prime factors factors that are also prime numbers. Write your number out in terms of its lowest common factors. Then, look for matching pairs of prime numbers among your factors. When you find two prime factors that match, remove both these numbers from the square root and place one of these numbers outside the square root.

As an example, let's find the square root of 45 using this method. Simply remove the 3's and put one 3 outside the square root to get your square root in simplest terms: 3 Sqrt 5. From here, it's simple to estimate. We have several 2's in our square root. Since 2 is a prime number, we can remove a pair and put one outside the square root. From here, we can estimate Sqrt 2 and Sqrt 11 and find an approximate answer if we wish. Method 2. Using a Long Division Algorithm.

Separate your number's digits into pairs. This method uses a process similar to long division to find an exact square root digit-by-digit. Though it's not essential, you may find that it's easiest to perform this process if you visually organize your workspace and your number into workable chunks.

First, draw a vertical line separating your work area into two sections, then draw a shorter horizontal line near the top of the right section to divide the right section into a small upper section and a larger lower section.

Next, separate your number's digits into pairs, starting from the decimal point. For instance, following this rule, 79,,, Write your number at the top of the left space.

As an example, let's try calculating the square root of Draw two lines to divide your workspace as above and write "7 It's O. You will write your answer the square root of Find the largest integer n whose square is lesser than or equal to the leftmost number or pair.

Start with the leftmost "chunk" of your number, whether this is a pair or a single number. Find the largest perfect square that's less than or equal to this chunk, then take the square root of this perfect square. This number is n. Write n in the top right space and write the square of n in the bottom right quadrant. In our example, the leftmost "chunk" is the number 7.

Write 2 in the top right quadrant. This is the first digit of our answer. Write 4 the square of 2 in the bottom right quadrant. This number will be important in the next step. Subtract the number you just calculated from the leftmost pair. As with long division, the next step is to subtract the square we just found from the chunk we just analyzed. Write this number underneath the first chunk and subtract, writing your answer underneath.

In our example, we would write 4 below 7, then subtract. This gives us an answer of 3. Drop down the next pair. Move the next "chunk" in the number whose square root you're solving for down next to the subtracted value you just found. Next multiply the number in the top right quadrant by two and write it in the bottom right quadrant.

In our example, the next pair in our number is "80". Write "80" next to the 3 in the left quadrant. Next, multiply the number in the top right by two. Fill in the blank spaces in the right quadrant.