» » how to solve any root sum in 30 seconds maths Trick

how to solve any root sum in 30 seconds maths Trick

By • May 22, 2017 • • Comments : 0

हेलो दोस्तों आज मई आपको squire roots के बारे में कुछ जरूरी टिप्स बताऊंगा तो चलिए सीखते हैं।  मेरा नाम है राजा और आप सीख रहे हैं कुछ नया तो देर किस बात की Let's Start





Facts for Square Roots Math tricks :

  • Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
  • Square of a number cannot end with 2, 3, 7, and 8. OR number ending with 2 , 3, 7 and 8 cannot have perfect squareroot.
  • Squareroot of a number ending with 1 (1, 81) ends with either 1 or 9 (10’s compliment of each other).
  • Squareroot of a number ending with 4 (4, 64) ends with either 2 or 8 (10’s compliment of each other).
  • Squareroot of a number ending with 9 (9, 49) ends with either 3 or 7 (10’s compliment of each other).
  • Squareroot of a number ending with 6 (16, 36) ends with either 4 or 6 (10’s compliment of each other).
  • If number is of ‘n’ digits then square root will be ‘n/2’ OR ‘(n+1)/2’ digits.

Based on the facts, square root method can be calculated as follows:
  • Specific Method: This method shows how find square root of a PERFECT square.
  • General Method: This method shows trick to find square root of any of PERFECT of IMPERFECT Square.

Specific Method:

This shortcut method of Square Roots can be applied whenever number is perfect square.
Example:
Square root of 2209
  1. Number ends with 9, Since it’s a perfect square, square root will end with 3 or 7.
  2. Need to find 2 perfect squares (In Multiplies of 10) between which 2209 exists.
    Numbers are 1600(402) and 2500(502).
  3. Find to whom 2209 is closer. 2209 is closer to 2500. Therefore squareroot is nearer to 50
    Now from Step 2, possibilities are 43 or 47 out of which 47 is closer to 50
  4. Hence squareroot = 47.

Finding Square Roots with Duplexes using Vedic Mathematics
What is a duplex?
Duplex D is described in a procedure called ‘Dvandva Yoga’ explained in ancient Vedic Mathematics Sutras. In algebraic terms, duplexes can be computed by the following rules:
1. The duplex of a single digit is its square.  
D( a ) = a2
D(3) = 32 = 9
2. The duplex of a two-digit number is twice the product of the digits.
D( ab ) = 2ab
D( 25 ) = 2.2.5 = 20
3. The duplex of a three-digit number is the sum of twice the product of the outer digits and the square of its inner digit.
D( abc ) = 2ac + b2 = D(ac) + D(b)
D( 153 ) = 2.1.3 + 52 = 6 + 25 = 31
4. The duplex of a four-digit number is the sum of twice the product of the outer digits and twice the product of the inner digits. This rule works for all numbers with an even number of digits – working the duplexes inwards.
D( abcd ) = 2ad + 2bc = D(ad) + D(bc)
D(4316) = 2.4.6 + 2.3.1 = 48+6 = 54
5. The duplex of a five-digit number is the sum of twice the product of the outer digits, twice the product of the inner digits and the square of the central digit. This rule works for all numbers with an odd number of digits – working the duplexes inwards to the central digit.
D( abcde ) = 2ae + 2bd + c2 = D(ae) + D(bd) + D(c)
D(13465) = 2.1.5 + 2.3.6+ 42 = 10+36+16 = 62

Squaring a number using duplexes
The square of a number can be easily computed using duplexes.
Given a number 23187, we can find its square by adding the duplexes starting from the left and moving right.
i) (23187)2 = D(2) + D(23) + D(231) + D(2318) + D(23187)+ D(3187) + D(187) + D(87) + D(7)
ii) (23187)2 = 4 + 12 + 13 + 38 + 77 + 58 + 78 + 112 + 49  Fill the duplexes into a grid as shown below and add the columns of numbers. The last row gives the square of 23187.
iii) (23187)2 = 537636939
4








1
2








1
3








3
8








7
7








5
8








7
8







1
1
2








4
9
5
3
7
6
3
6
9
6
9

Finding the square root of a number using duplexes
The square root of an n digit number has n/2 digits if the number has an even number of digits and  (n+1)/2 digits if the number has an odd number of digits.
i)              Find the square root of 3844
                     |3   8 :    4     4  |
Divisor      12  |       :   2    0    |  Carry line
                     |   6   :   2         |  Result 
 Square root of 3844 = 62
  1. Starting from the right of the number, group the number in digit pairs.
  2. 38 is the leftmost pair.
  3. Find the nearest square to 38 and write down the square root of it as the first digit of the result.= 6 rem 2.
  4. Place the 6 on the result line and the remainder 2 on the carry line. Double the answer 6. This becomes the divisor 12.
  5. The next dividend is 24. Divide 24 by 12 to get a quotient of 2 with remainder 0.
  6. Place the 2 on the result line and the remainder 0 on the carry line.
  7. The next dividend is 04.
  8. Compute the duplex of the last result 2 and subtract it from 04.
  9. We have 4 – D(2) = 4 – 4 = 0
  10. This 0 signals that 62 is the square root of 3844.
 ii)             Find the square root of 264196.
                        |2 6    :     4     1     9     6    |
       Divisor  10  |        :   1    4      0     1      | Carry  
                        |     5  :   1     4      0     0     | Result
 Square root of 264196 = 514
  1. Starting from the right of the number, group the number in digit pairs.
  2. 26 is the leftmost pair.
  3. Find the nearest square to 26 and write down the square root of it as the first digit of the result.= 5 rem 1.
  4. Place the 5 on the result line and the remainder 1 on the carry line. Double the result 5. This becomes the divisor 10.
  5. The next dividend is 14. Divide 14 by 10 to get a quotient of 1 with remainder 4.
  6. Place the 1 on the result line and the remainder 4 on the carry line.
  7. The next dividend is 41.
  8. Compute the duplex of last result 1 and subtract it from 41.
  9. We have 41 – D(1) = 40. Divide 40 by 10 which results in a quotient 4 and a remainder 0.
  10. Place the 4 on the result line and the remainder 0 on the carry line.
  11. The next dividend is 09.
  12. Compute the duplex of last 2 results 14 and subtract it from 09.
  13. We have 09 – D(14) = 1. Divide 1 by 10 which results in a quotient  0 and a remainder 1.
  14. Place the 0 on the result line and the remainder 1 on the carry line.
  15. The next dividend is 16.
  16. Compute the duplex of last result 4 and subtract it from 16.
  17. We have 16 – D(4) = 16 – 16 = 0.
  18. This 0 signals that 514 is the square root of 264196. 
iii)           Find the square root of 17 up to 3 dp.
                        |1  7   .       0     0     0     0   
       Divisor  8    |          :   1    2     3    2          | Carry   
                         |    4  .   1     2     3                 | Result
 Square root of 17 = 4.123
  1. Start with 17.
  2. Find the nearest square to 17 and write down the square root of it as the first digit of the result.= 4 rem 1.
  3. Place the 4 on the result line and the remainder 1 on the carry line. Double the result 4. This becomes the divisor 8.
  4. The next dividend is 10. Divide 10 by 8 to get a quotient of 1 with remainder 2.
  5. Place the 1 on the result line and the remainder 2 on the carry line.
  6. The next dividend is 20.
  7. Compute the duplex of last result 1 and subtract it from 20.
  8. We have 20 – D(1) = 19. Divide 19 by 8 which results in a quotient 2 and a remainder 3.
  9. Place the 2 on the result line and the remainder 3 on the carry line.
  10. The next dividend is 30.
  11. Compute the duplex of last 2 results 12 and subtract it from 30.
  12. We have 30 – D(12) = 26. Divide 26 by 8 which results in a quotient 3 and a remainder 2.
  13. Place the 3 on the result line and the remainder 2 on the carry line.
  14. We stop here as we have a result up to 3 dp.  = 4.123 

Share this:

Post a Comment

Kuch bhi pooncho yar ! Tumhaare liye hi to banaya hai comment box

Subscribe to: Post Comments ( Atom )
 
Copyright © 2025 Learning Raja. Designed by OddThemes