Question

Perfect square number between 20 and 30 is/are ?

Answer 1

Hint: In order to determine the perfect square numbers between \[20\] and \[30\]. First, we have to list down all the numbers between \[20\] and \[30\] then we need to check the perfect square numbers among them. Now, we have to eliminate those numbers which are prime numbers. If it is expressible as a product of two same numbers it is a perfect square.

Complete step by step solution:
In this problem, we need to analyse the perfect square number between \[20\] and \[30\].
First, we have to list down all the number between \[20\] and \[30\]:
\[21, 22, 23, 24, 25, 26 , 27, 28 \] and \[29 \] --------(1)
We know that the perfect square numbers of units digit always end with \[0 ,1 ,4 ,5 ,6 ,9\].
From equation (1),
We have to check whether the number of unit digits ends with \[0 ,1 ,4 ,5 ,6 ,9\] or not.
Therefore, the numbers between \[20\] and \[30\] end with unit digits are:
\[21,24,25,26\] and \[29\].
Now, we will check these numbers one by one for a perfect square.
\[21 = 3 \times 7\] , \[24 = 2 \times 12\] , \[25 = 5 \times 5\] , \[26 = 2 \times 13\] and \[29\] is a prime number, not a perfect square.
Thus, we can see that the number \[25\] is expressible as a product of prime numbers in pairs i.e. \[5 \times 5\].
Hence,\[25\] is the perfect square number between \[20\] and \[30\].

Note:
Perfect square number is a number which is a square of some number.
Since, when some number is multiplied by itself we obtain a number that is a perfect square .
For example:
\[
  {5^2} = 5 \times 5 = 25 \\
  {7^2} = 7 \times 7 = 49 \\
\] where \[5\] and \[49\] are perfect square numbers.
Perfect square numbers always end in (i.e. unit digit) \[0,1,4,5,6\] and \[9\].
Prime numbers are those numbers which are either divisible by \[1\] and itself. Prime numbers can never be perfect squares. For example \[29\] is a prime number which is not a perfect square.