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Exercise 40 - Example (Page 1) 		Home
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Find the square root of 180625 by division method.
    425       
    4|18,06,25
      |16-------(Step 1)
  82|206
      | 164-------(Step 2)
845|  4225-------(Step 3)
      |  4225
         0

square root of 180625 is 425

Group the digits in pair starting from right.
Step 1: Calculate the nearest perfect square for the first pair 18. Ex: 4 x 4 = 16
Put 4 in the top and side, and multiply 4 x 4 = 16 and write it below 18.
Subtract 16 from 18 = 2, and bring the next pair down. Ex: 206
Step 2: Multiply 4 by 2 = 8 and write 8 in the side. Find the next number by trial, 81 x 1 = 81 < 206
82 x 2 = 164 < 206, 83 x 3 = 249 > 206. hence the next number is 2, place it in the top next to 4 and in the side next to 8.
Subtract 164 from 206 = 42, and bring the next pair down 25. Ex: 4225
Step 3: Multiply 2 by 2 = 4 and write 4 in the side next to 8 as 84 instead of 82. Find the next number by trial, 841 x 1 = 841 < 4225
843 x 3 = 2529 < 4225, 844 x 4 = 3376 < 4225, 845 x 5 =4225. hence the next number is 5, place it in the top next to 42 and in the side next to 84.

Answer = 425
Find number "n", by which 1250 can be multiplied to make it a perfect square.
2|1250
5|625
5|125
5|25
   5

1250 = 2 x 5 x 5 x 5 x 5 = 2 x 54

                                        
1250 = 2 x 54

                     
1250 = 2 x 52
The number is 2.
1250 x 2 = 2500, which is a perfect square.
Square root of 2500 is 50.
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