# The Mystery of Finding the Square Root of 7

As humans, we have always been intrigued by numbers and the mysteries that they hold. One such mystery is finding the square root of 7. But before we delve into the mystery of it all, let’s first understand what a square root is.

A square root is basically the inverse operation of squaring a number. In simpler terms, it is the value that you multiply by itself to get a given number. For example, the square root of 16 is 4 because 4 multiplied by itself gives us the result of 16.

Now, coming back to the mystery of finding the square root of 7. The reason why it’s a mystery is that there is no exact value for it. Unlike other numbers like 4, 9 or 16, which have a whole number as their square root, 7 doesn’t have an exact whole number square root.

To understand why this is the case, we need to understand the concept of irrational numbers. An irrational number is a number that cannot be expressed as a fraction of two integers. These numbers have an infinite number of non-repeating decimals, making them unending and non-terminating.

The square root of 7 is one such example of an irrational number. It has a decimal value of approximately 2.6457513… and the decimal goes on forever without repeating any pattern. This makes it impossible to express the square root of 7 as a finite decimal or a fraction.

However, even though we cannot express the square root of 7 as a whole number or a finite decimal, we can still use various methods to approximate it to a certain degree of accuracy. One such method is the long division method or the Babylonian method.

The Babylonian method involves using an initial guess and then refining that guess through repetitive calculations until we reach a satisfactory level of accuracy. Let’s take a look at how it works.

We start with an initial guess, let’s say 2. We then divide 7 by 2, giving us 3.5. We then take the average of our initial guess and the result we got from dividing 7 by 2, which is (2+3.5)/2=2.75. We then repeat the process, dividing 7 by 2.75, giving us a result of 2.54. We then take the average of 2.75 and 2.54, which is (2.75+2.54)/2=2.645.

We can continue this process for as many iterations as we want until we reach a level of accuracy that we are satisfied with. Using this method, we can approximate the square root of 7 as 2.6457513, which is very close to the actual value.

Another method we can use to approximate the square root of 7 is by using a calculator or a computer program. Modern calculators and computers have built-in functions that can calculate the square root of any number to a high degree of accuracy. Using these tools, we can get an approximation of the square root of 7 to as many decimal places as we want.

In conclusion, while the mystery of finding the square root of 7 may seem daunting at first glance, it is not impossible to solve. While we cannot express it as a finite decimal or a whole number, we can use various methods to approximate it to a high degree of accuracy. The Babylonian method and modern calculators and computers are just two such methods that we can use to unravel this age-old mystery.