Simplest method to find root of non perfect square

Simplest method to find root of non perfect square

Many students found problem to solve square root of non perfect square values. But here we teach you the simplest method to solve the non perfect square value in just 2 minutes.

                    But for this you should learn below given data-

 Then as you all know that in mathematics for the simple or quick solution of any question an formula is required. So for the solution of non perfect square root we also have a formula to solve it by easy manner.

Formula=
                          Square root =

You have to split that non perfect square number in two parts one is x and other is y.

But you have to split in that way in which x always become a perfect square. This method gives the approximate value but they are very near to exact value of root. It is the easiest way to solve non perfect squares.

Steps to solve these types of square roots

1. Firstly write the number in square root.

2. Then break that number into two parts and there is one condition that one part of that number is closest perfect square .

3. When you broke that number then apply formula on that and get your answer.

Let us take an example first 

Q:1. Find the square root of 7?

Sol. Firstly write it in square root form i.e. √7

2. Break is into two parts in which one part is closest perfect square. You can make different parts as you own thinking. In this case let we make 

√7 = √(9 - 2)

In it + or - is as per your parts construction.

Then apply formula on it

In this question when we break √7 then 4 behaves as X and 3 behaves as Y.

             √(9 -2) = √9  - 2/2√9   

√9 = 3

                       = 3 - 2/2*3.    

             

= 3 - 0.75

= 2.667 ans. Approximately = √7.

Let us take an another example

Q:2. Find the square root of 47?

Sol. Again same steps will be followed 

1. Write it in root form i.e. √(47

2. Break it into two parts in which one part is nearest perfect square . Nearest perfect square to 47 is 49.

√(47 = √(49 - 2) 

3. Apply formula on it  we get ,

√(49 - 2) = √49 - 2/2*√49

= 7 - 2/2*7

= 7 - 0.142

= 6.85 ans.

Let us find out another square root by this method

Q:3. Find out the square root of 378?

Sol. 1. Write it in root form i.e.√378

2. Break it into two parts in which one part is nearest perfect square to that number i.e. 361 which is a square of 19.

√378 = √(361 + 17)

3. Applying the formula 

√(361 + 17) = √361 + 17/2*√361

= 19 + 17/38

= 19.44 ans

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