How to find square roots without long Division method

I wanted to share this post from a long time but somehow this couldn't be possible, but now here it is,

How to find square roots without long Division method

                                      

yes..!!

There is one method i.e. approximation method but this wouldn't​ lead us towards exact solution at all time,

 " Confuse...??"

don't worry see this example.

Q. Find √23

Sol. using approx. method 

      A perfect square before 23 is 16  and just next perfect square is 25.

so this can be written as 

 
 √16 < √23 < √ 25

      4  <  4.7or 4.8 < 5 ( this is an approximation)

but  √23 = 4.79583

 • And now our short method to evaluate square root of √23...

Next highest square root is √25 

so,

let 23 = A

      25 = B

• our formula of finding square root of will be 

 •   √A = √ B + (A - B)/ 2×√B

 √23   = 5    + (23-25)/ 2× 5

          = 5    - 2/ 10 

          = 5   - 0.2

          = 4.8

 •    let's have an another example for √45
so,
45 = A
49 = B
putting values into Formula

√A =  √ B + (A - B)/ 2×√B
√45 = 7  +  ( 45-49) /2×7
       =  7 -  4/14
       =  7 - 0.28571
       =  6.71429      

now by evaluating from calculating
√45 = 6.7082 ≈ 6.71429

so this Method is giving us nearly equals to exact values.

   • No doubts this method  is easy than long Division and also giving answer to satisfactory manner, But it requires​ practice to become perfect. Try at least for twice or thrice with different values.

So this is our today'as tutorial of finding square root of any number without our traditional method.
Have a look at some best tutorials From Math's Buddies:

• Math's Magic Square

• Euclid's Math for polyhedron

Now over to you, let me know how you have found this tutorial helpful to you, by commenting.

Short Trick to find Square

page contents

The content which I'm going to share in this tutorial is a very demanding​ by readers and also proven to become a major tool for math enthusiast.

This post is also refers to one who struggles with finding huge squares calculations.

so, the topic starts here,

• Square roots : Trick

Short trick to find squares

tricks to finding squares may be varies with given number categorically.

• Square of Number ends with 5:

Numbers which ends with 5 like 25, 35, 45, 65 etc the square of these numbers can be found easily without actual multiplication.
How..??

look at Solution below

25² = 625
steps:
1. Take 1st digit and multiply it by next highest digit.
say, 2 × 3 = 6

2. Square if ones digit i.e. 25 should place at the end of the answer.
say, 5² = 25
 hence the answer ​is 625.
See below image for better​ understanding.

Have a look at Math's Buddies featured posts:

• Short trick to find roots of cubic polynomial​

• Top 10 interesting facts about Pi (π)

Let's move for some larger numbers which are greater then 100

yes of course we have a trick...stay with me and look below.

113²

= 12769 ( by multiplying method )

try this one :

= 113²

 113 + 13 = 126

and 13² = 169

   now we're having two numbers 

126 and 169 now add these numbers in following manner:

  

  126  

+    169

=12769            voila...!!! answer is here 

  •  This seems to be lengthy method but trust me once if you get into this you will find this most convenient methods to find squares.

see another example:

126²

126 + 26 = 152

26² = 676

now 

= 152

+     676

=  15876

hope you enjoyed this post, feel free to share with your friends and with those who need this.And also let me know what type of tutorial do you want here.

Thanks