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**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.

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