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Shortcuts On Finding The Square Root

Updated on November 30, 2009

Shortcuts on Finding Square Roots

Finding the square root of a 4-digit perfect square ending in 5

Sample Problem Number One :

Find the square root of  5675

Step One :   Drop the first two digits of the square .   56

Step Two:    Find the largest square root of the remaining digits. This is the first digit of

                    The square root. Find the largest root in 56 :

                      7 X 7  =  49

                     The first digit in the square root is 7

Step Three :  Append 5 to 7 =è75

Therefore the square root of 5625 is 75.

Sample Problem Number Two:

Find the square root of 7225

Step One :       72

Step Two :      Find the largest square root  in 72.

                       8  X  8   =   64

                      The first  digit in the square root is 8.

Step  Three :  Append   5 to 8

Therefore the square root of 7225  is   85.

Sample Problem  Three :   Find the square root of  3025

Step One :   30

Step Two;   Find the largest square root in  30

                      5 X 5  =   25

                     The first digit  in the square root is 5.

Step Three :   Append   5 to 5

Therefore the square root of  3025   is   55.

Sample Problem  Number Four : Find the square root of  9025

Step One : 90

Step Two : Find the largest square root in 90

                  9 X 9  =   81

                  The first digit in the square root is 9.

Step Three :   Append  5  to  9

Therefore the square root of 9025 is 95.        


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    • profile image


      4 years ago

      Oh my! Thank you so much for this shortcut! It really helps me a lot!

      Thank You!!! :)

    • profile image


      6 years ago


    • profile image


      7 years ago

      Thanks for Tips of Shortly Find Squre Root

    • aweswan profile image


      7 years ago from TN

      It is truly interesting the many ways to find the square root of a number, some are simple as you show here and others are explained in such a complex language. But there is another way to find the square root of numbers that are not a perfect square and have decimals. It is by using the algorithm method, and it really is not that complex at all. Before computers it was taught in high schools. I have it explained as best as I can on my hub so I won't go into it here, check it out if you like.

    • profile image


      7 years ago

      thank you for helping me to find square root of numbers!but what happen when the number is not a correct square

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi Taleb80 I am glad to hear from you. Thanks for dropping by and appreciating this hub. Blessings to you and regards.

    • Taleb80 profile image

      Taleb AlDris 

      7 years ago

      Sure It is useful so I should vote.

      Thanks for sharing your Math skills.

    • Larry Fields profile image

      Larry Fields 

      7 years ago from Northern California

      Thanks, cristina. I hadn't seen your square-root method before. To answer raviindra's question, there is a slightly more general method for finding the square root of four-digit perfect squares.

      Example: Find the square root of 2401.

      Step 1. This time, temporarily drop the LAST two digits, and temporarily replace them with zeros.

      Result = 2400.

      Step 2. What's the largest two-digit number, ending in zero, whose square is less than or equal to 2400?

      Result = 40.

      Write down "4_".

      Step 3. Now look at the last digit, which is a "1".

      Step 4. How many two-digit perfect squares end in a "1"?

      Step 5. The two possible results are 1, whose square root is obviously 1; and 81, whose square root is 9.

      Step 6. Add the two square roots from Step 5 to the Step 2 result. The two results are:

      4_ + 1 = 41 and 4_ + 9 = 49

      Step 7. Test ONE of the two square root candidates from the previous step, which are 41 and 49, in this example.

      The square of 41 is NOT 2401.

      Therefore the square root of 2401 is 49.

      Note. If the four-digit perfect square ends in "4", "5", or "9", Step 7 will be faster, and you can do the entire calculation mentally. You won't need a calculator or a slide rule.

    • profile image


      7 years ago


    • profile image


      7 years ago


      Its really good one

    • profile image

      Ajith kumar 

      8 years ago

      Thank u and it is very simple..what abt the other numbers in units place??

    • profile image


      8 years ago

      thank u but what about other numbers that are placed in last digit place

    • profile image


      8 years ago

      its interesting &very goooood,easy method...

      but what abt other numbers which r not perfect squares &

      not ending with 5...

    • profile image


      8 years ago

      vvvvvvv gooooood method!!!!!!!!!!!!!!!!!!!!!!!!

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      9 years ago from Manila

      Hi Teresa thank you for taking time to read this hub. YOur comment is well-appreciated, God bless you. A merry christmas to you and your family.

    • Teresa Laurente profile image

      Maria Teresa Rodriguez - Laurente 

      9 years ago from San Antonio, Texas, U.S.A.

      This is fun. How about Statistics. Maybe you can share it too. Thank you for sharing this. More power.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      9 years ago from Manila

      Hello Heavengates it is nice to hear your comment on this Math hub. I am happy you like it. Merry Christmas also to you and your family. May you have the best of the season. God bless.

    • Heavensgates profile image


      9 years ago

      cristina, thank you for helping me figure this out again! It's been some time, math is and can be fun, but I opted for speaking and writng. Keep up the good work! Merry Christmas to you and your family!!!


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