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Tricks to calculate square roots easily
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:
- 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.
- 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.)
- 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.
- 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.
Interesting reading - related to what you are reading
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
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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....
What is your preference on using math tricks / short cuts?
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.
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