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# Perfect square number between 20 and 30 is/are ?

Last updated date: 21st Mar 2023
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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.