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Square Roots Calculator and Square Calculator

Looking for a faster, more convenient way to find square and square roots when doing homework or for mathematical applications? Check out our square roots calculator and square calculator.

What is a Square Calculator?

Our square calculator is aptly named: it is simply an online resource used to calculate the square of a number. A square is defined as the product of any number multiplied by itself (x2). For example, the square of 12 is 144 (the product of 12 times 12).

What is a Square Roots Calculator?

A square roots calculator finds the number that, when multiplied by itself, would give you the number you are starting out with. For example, the square root of 144 is 12, because 12 times 12 equals 144. Of course, -12 times -12 is also 144. Therefore, every number actually has two square roots. One thing to be aware of when using any calculator with square root functionality is that it will probably only give you the primary square root—that is, the positive square root. For most applications, the positive root is all you need. However, for mathematical problems remember that the second negative square root is also needed for the correct answer!

Online vs Handheld Calculators

While many of us grew up using a handheld calculator with square root keys, now we also have an online calculator square root option. In most cases, the online calculator is more useful. You might not always have a handheld calculator at the ready when you need to know a square or square root, but you probably do have your smartphone or tablet, which will allow you to access the online tool anywhere you have wifi or data service. Plus, most online calculator square root tools are easier to use than their handheld counterparts. Instead of worrying about pushing the calculator keys in the proper sequence, all you have to do online is type in your number and click a single button.

Square Root Calculator History
Modern technology has made many aspects of our lives much easier, including mathematics. Many mathematical tasks that used to take hours of tedious calculations can now be accomplished in just a few minutes using a computer or calculator. In order to better appreciate what calculators save us from, it is interesting to look at the history of modern tools like the square root calculator.

Simplest Manual Square Root Method
The simplest method for finding square roots manually is just to guess. Pick a number, square it, and see if the result is too low or too high. Of course, it will be easier if you make an educated guess based on the closest perfect squares (numbers that can be expressed as a whole integer times itself). For example, if you want to find the square root of 18, begin by finding the closest perfect squares, which are 16 and 25. The square roots of these numbers are 4 and 5. So, because 18 is between 16 and 25, we know its square root must be between their square roots, that is, between 4 and 5. It should be closer to 4 because 18 is closer to 16. Take a guess…let’s say 4.3. 4.3 times 4.3 is 18.49. That’s more than 18. So make your next guess a bit lower. 4.2 squared is 17.64…too low! Now try something halfway between the two guesses: 4.25. 4.25 squared is 18.0625. Close enough!

Oldest Manual Square Root Method

The oldest method for finding the square root of a number is known as the “Babylonian Method” after the civilization that historians believe first used this method. It is also sometimes called “Heron’s Method” after the Greek mathematician that recorded the first detailed description of the method. This method is basically a fancier way of doing the simple guessing method. It uses an algorithm to calculate the square root based on the average of an underestimate and overestimate of the root.

Modern Square Root Calculator

Of course, when you want a fast and accurate square root calculated to multiple decimal places, a modern square root calculator is by far your best option. These types of calculators first began to crop up in the 1970s, and a calculator with all the bells and whistles could be quite expensive. Nowadays, however, you can find square roots even more easily without special equipment, just by using an online calculator.

See our Cube Root Calculator

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