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What are square number ?
⇨ When any number is multiplied by itself then the number obtained is
called square of that number.
Ex. 45 x 45 = 2025, Here 2025 is the square of 45.
Different methods of making perfect square.
⇨ There are four different methods of making perfect square. These are
as follows;
⇨ By Addition Method
⇨ In this method we can make any number
a perfect square number by adding some number. For example, let us take
23, which is not a perfect square.
We know that 25 is the nearest square number of 23. So to make it a
perfect square we have to add 2 in 23 so that it become 25, which is a
perfect square number of 5.
⇨ By Subtraction Method
⇨ In this method we can make any
number a perfect square number by subtracting some number. For
example, let us take 23, which is not a perfect square.
We know that 16 is the nearest square number of 23. So to make it a
perfect square we have to subtract 7 from 23 so that it become 16,
which is a perfect square number of 4.
⇨ The above motioned methods are not useful for big
number.
⇨ By Division Method
⇨ In this method we can make any number a
perfect square number by dividing with some number. For example,
let us take 6300, which is not a perfect square.
⇨ Here we have to find the prime factors of 6300.
⇨ 6300 = 2 x 2 x 3 x 3 x 5 x 5x 7
⇨ From the prime factor we can see that only 7 is unpaired so to
make 6300 a perfect square we have to divide 6300 by at
least 7 to get a perfect square number 900 (square of
30).
⇨ By Multiplication Method
⇨ In this method we can make any number a
perfect square number by multiplying with some number. For
example, let us take 6300, which is not a perfect
square.
⇨ Here we have to find the prime factors of 6300.
⇨ 630 = 2 x 2 x 3 x 3 x 5 x 5x 7
⇨ From the prime factor we can see that only 7 is unpaired so to
make 6300 a perfect square we have to multiply 6300 by at
least 7 to get a perfect square number 44100.
How to check is there any perfect square in any sequence ?
⇨ To check is there any perfect square in a sequence we have to go
through prime factorization method as mentioned above.
For example, let 225 is a number in sequence, to check whether it is
perfect square or not we have to find its prime factor.
⇨ 225 = 5 x 5 x 5 x 5
⇨ As all prime factors are in pair indicates 225 is perfect square
(square of 15), If any of the factor is unpaired indicates it is not
a perfect square.