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Tricks to calculate square roots easily

Updated on July 5, 2013

Square Root Math Tricks

Math tricks to calculate square roots at your finger tips! No need for any gadgets and still square root answers will be ready in no time. Calculating square root is very difficult and requires lot of time & efforts if we are not to use calculator and other gadgets. Here is the math trick for square roots.

This is a summary on how to go about calculating squares / square roots of any number just by looking at it and not having to do any calculation larger than multiplying 9 with 9. The same square root math trick applies even for calculating square root of a "non perfect square" large number. This would make life of students very easy.

The square root math trick is to lay out rules on establishing the expected structure of the square roots (i.e. how may digits and where to put decimal point), then to go for actual calculation of the square root. These square root tricks are particularly useful for those preparing for competitive exams like GMAT, GRE, CAT etc.

Establish the structure of the square roots - how many digits and where to put decimal point?

This square root math tricks is established that number of digits in a square root would depend on how many digits the square has. Also, in case of fractions, the position of decimal point in square would would directly affect where do we put decimal point in square root.

Pointers to use the square root trick are listed below:

  1. The number of digits before decimal point would reduce to half when we take the square root of the number.(i.e. the square root of 1446.78 would have 2 digits before decimal number). This math trick would be applicable directly when the numbers of digits before decimal point are even.
  2. In case of odd number of digits before decimal point, the square root would still have half of the numbers but that half needs to be rounded up to the next integer. (i.e. square root of 144.678 would have two digits before the decimal point.)
  3. The number of digits after the decimal point would reduce to half when we take the square root of the number.(i.e. the square root of 1446.78 would have 1 digits after decimal number). This math trick would be applicable directly when the numbers of digits before decimal point are even.
  4. For numbers with odd digits after decimal point, the square root would be an irrational number, because any square of a whole rational number would have even digits only after the decimal point.

Let us summarize these rules with help of an image

Visual explanation of the above rules to make them perfectly clear!

Understand the structure of square root - summary of square root tricks for structure

tricks to derive squares easily
tricks to derive squares easily

Get the best math resources here!

Try out what your are looking for and you shall get the best resources for any math tricks!

Nature of the square root - whether the answer would be rational or irrational?

Having established whether a number is perfect square or not in previous step, its very easy then to know whether the expected answer (i.e. the square root) would be rational or irrational, the logic has been explained below:

  • For the numbers not exact squares of another whole number, their square root is always irrational. (i.e. the square root would have endless digits after decimal point and would not have any repeating patterns in those digits.)
  • Also, a number is odd number of zero's at the end, would never have a rational square root
  • For the rest of the numbers the square root would be rational.

I have a question for you....

calculate square root easily
calculate square root easily

What is your preference on using math tricks / short cuts?

See results

Square root would be even or odd?

This trick defined rules as to when the square root can be even and odd given various digit arrangements of the number we want to derive square root of.

  • Square root is odd when a perfect square is odd
  • Square root is even when a perfect square is even

Last digit of the square root - depends on the last two digits of the square

This trick is all about establishing last digit of the square root based on the last two digits of the square.

  • Number with last digits as 2, 3, 7 or 8 are not exact squares and inturn would result in an irrational number when their square root is calculated
  • Also, there is a direct relation between last digit of the number and last digit of its square root, as follows:

    number 1, square root 1 or 9

    number 4, square root 2 or 8

    number 5, square root 5

    number 6, square root 4 or 6

    number 9, square root 3 or 7

  • When the second last digit (from right) is even and the last digit is 6, the number is not a perfect square (i.e. 346 is not a perfect square)
  • When the second last digit (from right) is odd, the last digit has to be 6 for the number to be a perfect square. (i.e. numbers ending with 34, 59, 11 are not perfect squares)
  • When a number is even, and its last two digits taken together are not divisible by 4, that number is not a perfect square. (i.e. numbers ending with 42, 86, etc. are not perfect squares)

Finding Squares Easily

calculate squares easily and fast

You know the squares of 30, 40, 50, 60 etc.

but if you are required to calculate square of 31 or say 61 then you will scribble on paper and try to answer the question.

Can it be done mentally?

Some of you will say may be and some of you will say may not be.

But if I give you a formula then all of you will say, yes! it can be.

What is that formula….. The formula is simple and the application is simpler.

Say you know 60sq = 3600

Then 61sq will be given by the following

61sq = 60sq + (60 + 61) = 3600 + 121 = 3721

or Say you know 25sq = 625 then 26sq = 625 + (25 + 26) = 676

Like above, you can find out square of a number that is one less than the number whose square is known.

I do admire comments from the readers more than the likes, reason being, that's the only way I get to know whether I am doing everything right or not. So please drop in a word and it would mean the world to me

© 2012 kpp2385

So what do you think huh? - feel free, be frank

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    • profile image

      varun 2 years ago

      But if iwant square of 24 then .

    • profile image

      ketulpatel2385 2 years ago

      Wish I had all these tricks in high school! But very interesting approach to mathematics

    • profile image

      ketul2385 2 years ago

      Excellent and informative hub. Loved it.

    • profile image

      anonymous 4 years ago

      Grete lens....!blesss...ed

    • profile image

      anonymous 4 years ago

      good job.

    • profile image

      anonymous 4 years ago

      its good tricks for sqrt............thanks

    • EdTecher profile image

      Heidi Reina 5 years ago from USA

      Excellent tips for calculating square roots. I've never tried Vedic math before.

    • moanaparker lm profile image

      moanaparker lm 5 years ago

      Yeah it's a real success way.. Again impressive tricks

    • bigjoe2121 profile image

      bigjoe2121 5 years ago

      I love that some people have minds that think like this. Mine doesn't though, so I just leave it to those people.

    • profile image

      anonymous 5 years ago

      Great lens! Blessed!

    • profile image

      antoniow 5 years ago

      Very nice lens, thumbs up!

    • mel-kav profile image

      mel-kav 5 years ago

      Great tips! Bookmarking this for my daughter!

    • MartieG profile image

      MartieG aka 'survivoryea' 5 years ago from Jersey Shore

      Nicely done! It's been years since I have figured square roots and I wish I had known this them! :>)

    • RhondaAlbom profile image

      Rhonda Albom 5 years ago from New Zealand

      Great tips for squares and roots. Blessed.

    • VeseliDan profile image

      VeseliDan 5 years ago

      This is really useful!

    • profile image

      anonymous 5 years ago

      this is very interesting... really liked the relationships between the square root and squares in terms of last digits.. excellent content

    • wcjohnston profile image

      wcjohnston 5 years ago

      Thanks, I will share this with my daughter

    • profile image

      john00825 5 years ago

      nice way to dealing with squares and square roots

    • profile image

      jazziyarbrough 5 years ago

      Thank you, great math tricks to remember. Thanks for sharing

    • MariaDSk profile image

      MariaDSk 5 years ago

      Very nice.Square roots really annoy me when calculating in mind only, lacking a concrete formula and such.

    • srsddn lm profile image

      srsddn lm 5 years ago

      I appreciate your effort to put the tricks in a lens. A good stuff for my young son to use. Thanks.

    • loki1982 lm profile image

      loki1982 lm 5 years ago

      Nice lens

    • profile image

      trendydad 5 years ago

      seems interesting, i may to purchase the book to relate better

    • profile image

      anonymous 5 years ago

      Very nicely presented and sounds like a lot of fun playing with numbers!

    • profile image

      TerryNeal 5 years ago

      Great way to calculate squares , who knew just add to the known square number.

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    • SecondHandJoe LM profile image

      SecondHandJoe LM 5 years ago

      This is fascinating Ketul! I did it! Fun, thanks!

    • profile image

      Alohagems 5 years ago

      Very good, very helpful to students. Now learning perfect square is easier

    • Virginia Allum LM profile image

      Virginia Allum LM 5 years ago

      fantastic -must show it to my daughter who understands maths much,much better than I do

    • profile image

      squidsmc 5 years ago

      how about using the same logic for multiplication of numbers near the base of 10 or any of it's power. I think the same logic would be useful there

    • profile image

      smcsquid 5 years ago

      why don't you also explain the logic behind this short cut to make it more authentic for users?

    • profile image

      anonymous 5 years ago

      nice method but doesn't it look like having limited application? but yes, in any case it would be very useful for competitive exams...

    • profile image

      anonymous 5 years ago

      do you have anything on solving equations using vedic mathematics? please post that as well, I have been looking for that since long

    • profile image

      anonymous 5 years ago

      very interesting.. even for small business owners...

    • profile image

      anonymous 5 years ago

      excellent method.. would be very useful for students... specifically in competitive exams