# Easy Ways to Calculate Square Roots 1 2 3 Manually

Square roots 1 2 3, how is to calculate it manually? There are many roots in math and square roots are roots with the lower value. Logically, it should be easier to find the results compared to the others. Unfortunately, it is still difficult for many people except you have memorized it. Different from other calculations in which there are two or even more numbers as the hint, in square roots, there is only a number. That’s why; people may prefer using faster methods like using a calculator or mathematic table.

There are some methods to let you calculate square roots manually in a faster way. When you have been accustomed to it, no matter how big the number it, it is possible to find the results only in some minutes. The methods are as follow.

## Prime Factorization

Finding out the results of square roots can be through a method named Prime Factorization. It is by turning numbers under the root sign to a square form in a multiplication of a certain prime number. For example, you want to look for the result of the 130 square root. Well, it is known actually that this number has no integer square root result. But you should not worry; it can still be predicted through Prime Factorization.

So, the first thing to do is by looking for the factors using the lowest prime number. It is found that 130 is a result of 2 x 65. You can take a look at 65 now and then it is found that the number is a multiplication result of 5 and 13. Knowing the factors of 130 is 2 x 5 x 13, the square root can be found out.

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## The General Method

In this method, a number under the root sign must be divided into 2 digits starting from the end. You can try to find out the root from the number. Then, a multiplication operation is conducted along with diminution. To do this operation, you can use a general formation of a  + bx + c. There are some formulas generated from the formation above. For examples, there are X1 + X2 = –  , X1 – X2 =  , and still many more.

## Calculating the Number per Digit

If you want it to be more manual, you can do it by seeing the last digit of the number. there is an exact rule in which a number ended by 9, the square root result must be ended by 7 or 3. Meanwhile, a number ended by 4, the square root must be around 2 or 8. Until this point, you can actually predict the result. It is although to make it sure, manual multiplications must be done first.

However, how is the number has many digits? For examples, the digits are 4 or even 5. So, all you need to do is by seeing the 2 first number. for example, you need to find out the square root of 3,249. So, after knowing the result of 49 square root is 7, you need to predict the square root of 32. It is known that the lower-nearest number of 32 is 25 with the result 5. This way, the first digit of the result must be around 5. You can then check the result by multiplying 57 with the same number. Well, the result is definitely 3,249.

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Indeed, to make you really fluent in finding out the square root manually, there must be more practices. Besides, make sure that you are good enough in number multiplication at least from 1 to 10. So, this is how to calculate square roots 1 2 3.

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