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Solving Square Root is a child's play now


Finding Square Root of two or three-digit numbers is the easiest of all but when digits go on adding, we feel fearsome how to solve the puzzle within a second or two.

Friends! If you are in a similar situation where you have a long mathematical puzzle in which square root is just a part of it then let me take you out of this agony.


Square Root




Here we go….

First of all, go through these important facts:
  • Number ending with 2,3,7,8 will never give you a perfect square.
  • Number ending with an odd number of Zeros again has no perfect square.

Let’s try to solve the Square Root with the simplest method

Square Roots of four-digit number (For Perfect Squares):


Question1: √ 1024


Solution: Steps to solve:
  1. Break the number into two halves i.e. 10 and 24
  2. Take the second half i.e. 24 and check extreme last digit 4 appearing in the table:

  3. The extreme last digit 4 is coming after the squaring of 2 and 8.
    squareroott2
    This indicates that the answer will contain the last digit from these options 2 and 8.
  4. Now take the first half i.e. 10 and check the table again.
  5. Now check first half 10 lies in squares and choose the smaller value always.
  6. From 3 and 4, 3 is smaller and becomes the first digit of your answer.
  7. squareroott3

  8. Now we have options of first and last digit of answer 32 or 38.
  9. To find out the right option multiply 3 and 4.
  10. squareroott4

  11. Given 10<12 b=""> so choose the smaller option 32.
  12. squareroott5
  13. Square Root of 1024 is 32.



Question2: √ 2116


Solution:
  1. Break into two halves 21 and 16
  2. Take the second half and check extreme digit 6 appearing in the same table.
    squareroott6
    This indicated that the answer will contain the last digit from these two 4 and 6.
  3. Now take the first half i.e. 21 and again check the table.
  4. Now check first half 21 lies in squares and choose lower value always.
  5. squareroott7
  6. From 4 and 5, 4 is smaller and become the first digit of your answer.



  • First and last digit options of answers 44 and 46.
  • To find out the right option multiply 4 and 5

  • squareroott8



  • Given 21>20 so we choose greater value i.e. 46.

  • squareroott9



  • Square Root of 2116 is 46.

  • Square Root of Five Digit Number (For Perfect Squares):


    Question1: √ 13456


    Solution:
    1. Break into two halves such that you always left with two digits in the second half.
    2. 134      56
    3. Repeat steps 2 and 3 again.
    4. 6 appear in 4 and 6 and become options of answer’s last digit.
    5. squareroott10
    6. Now take first halve. The table is extended as we have now the first half containing three digits.
    7. squareroott11
    8. Now check first half 134 lies in squares and choose lower value always.
    9. squareroott12
    10. 11 becomes the first digit of the answer.
    11. The first and last digit options of the answer are 114 and 116.
    12. To find out the right option multiply 11 and 12
    13. squareroott13
    14. Given 134 >132 so choose greater value i.e.116
    15. squareroott14
    16. Square Root of 13456 is 116.

    Question2: √ 9025


    Solution:
    1. Break into two halves 90 and 25 such that you always left with two digits in the second half.
    2. 90      25
    3. Second half 25 is a perfect square of 5 so we have only one option of the last digit i.e. 5
    4. Take 90 and check where it lies and take the lower value always.
    5. squareroott15
    6. 9 will be your first digit of the answer.
    7. Square Root of 0925 becomes 95.

    Square Root of Six Digit Number(For Perfect Squares):


    Question1: √ 262144


    Solution:
    1. Break into two halves 2621 and 44 such that you always left with two digits in second half.
    2. 2621      44
    3. Check the second half 44 appear in table.
    4. Last Digit 4 appears at 2 and 8.
    5. squareroott16
    6. Now take first halve. Table is extended as we have now first half containing four digits .
    7. squareroott17
    8. Now check first half 2621 lies in squares and choose lower value always.
    9. squareroott18
    10. 51 becomes first digit of the answer.
    11. First and last digit options of answer are 512 and 518.
    12. To find out the right option multiply 51 and 52
    13. squareroott19
    14. Given 2621 < 2652 so choose smaller value i.e. 512 and is the answer.
    15. squareroott20

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