Mathematics Magic: Smart Work

Tricks on Square of a Number

( ट्रिक्स ऑन स्क्वायर ऑफ़ नंबर )

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Every one knows that Mathematics is every essential subject in our day to day life. So here are some basics tricks to find square of a number.

1.) To find square of a number ending with 5.

Numbers like 5,15,25,55,175,255,525, or _5 (where _ is an integer of any number of digit) type of number are ending with 5. To find square of such number following steps are to be followed :-

(i) Square the last digit number which is always 5, becomes 25.

(ii) Now, Let remaining digits be n and n+1 be a adjacent number to n.

(iii) Multiply n*(n+1).

(iv) So, your answer will become value of step(iii) and step(ii) combine i.e. n*(n+1)25.

Examples :-

You may check your answer by using calculator it will be same as done through this method.
(Condition applied, No calculation mistake of yours.)

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2.) Formation of arithmetic progression in square of number.

Arithmetic Progression is a sequence which has a constant difference between consecutive numbers.
example :- 2,5,8,11,14,17,and so on has common difference of 3.

On squaring natural number such arithmetic progression is seen on second times subtracting the sequence.

Example :-

We can get the natural number back as follows :-

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3.) Square of number adjacent to 5 multiple.

Number adjacent to 5 multiple are 4,6,99,101,74,76,44,46,etc.

Detail explanation :-

As 4 and 6 are adjacent number to 5 and 5 is multiple of 5 itself.

74 and 76 are adjacent number to 75 and 75 is multiple of 5.

99 and 101 are adjacent number to 100 and 100 is multiple of 5.

As we know the square of number ending with 5(First Trick) and also number ending with 0(like 10,100).

Steps :-

(i) Multiply number which is multiple of 5 let us say m with 2 and let it be n (where n=m*2).
(ii) Add +1 and -1 to the number n, which is obtain from step(i).
(iii) Now, add number (n+1) to square of number which is multiple of 5. It will square of (m+1).
(iv) Now, subtract number (n-1) to square of number which is multiple of 5. It will give square of (m-1).

Examples :-

(i) Square of 74 and 76.