28 = 2 * 2 * 7

For acquiring the perfect square number , 28 should be multiply by 7 .

Therefore 28 * 7 = 196 , which is a perfectly square ( it's square root is 14) .

Hence , answer is 7

Explanation:
To find the smallest number by which 28 should be multiplied so as to get a perfect square, we need to follow the steps given below:

Step 1: Write the prime factorization of 28.
28 = 2 × 2 × 7

Step 2: Identify the factors that are not in pairs.
28 = 2 × 2 × 7
The factor 7 is not in pairs.

Step 3: Multiply the number by the missing factor to get a perfect square.
In this case, we need to multiply 28 by 7 to get a perfect square.
28 × 7 = 196

Therefore, the smallest number by which 28 should be multiplied so as to get a perfect square is 7.

Explanation in Detail:
In mathematics, a perfect square is a number that can be expressed as the product of two equal integers. For example, 4 is a perfect square because it can be expressed as 2 × 2. Similarly, 9 is a perfect square because it can be expressed as 3 × 3.

To find the smallest number by which 28 should be multiplied so as to get a perfect square, we need to follow the steps mentioned above. Let's understand each step in detail.

Step 1: Write the prime factorization of 28.
The first step is to write the prime factorization of 28. Prime factorization means expressing a number as a product of its prime factors. Prime factors are the prime numbers that divide the given number exactly.

To find the prime factorization of 28, we can divide it by its smallest prime factor, which is 2. We get:

28 ÷ 2 = 14

So, 2 is a factor of 28. We can write 28 as:

28 = 2 × 14

Now, we can further divide 14 by its smallest prime factor, which is 2.

14 ÷ 2 = 7

So, 2 is a factor of 14. We can write 14 as:

14 = 2 × 7

Therefore, the prime factorization of 28 is:

28 = 2 × 2 × 7

Step 2: Identify the factors that are not in pairs.
The second step is to identify the factors that are not in pairs. In a perfect square, all the prime factors must be in pairs. If there is any factor that is not in pairs, we need to add it to the product to make it a perfect square.

In the prime factorization of 28, we can see that 2 is in pairs, but 7 is not in pairs. So, we need to add 7 to the product to make it a perfect square.

Step 3: Multiply the number by the missing factor to get a perfect square.
The third step is to multiply the number by the missing factor to get a perfect square. In this case, we need to multiply 28 by 7 to get a perfect square.

28 × 7 = 196

Therefore, the smallest number by which 28 should be multiplied so as to get a perfect square is 7.