Question

Find the smallest natural number by which 5808 should be multiplied so that the product becomes a perfect square.
A.1
B.2
C.3
D.11

Answer 1

Hint: In this question, we need to determine the smallest natural number which must be multiplied by 5808 so that perfect squared number results. For this, we will check the given options by multiplying with the number 5808 and see whether it results in the perfect square or not.

Complete step-by-step answer:
Let ‘y’ is the smallest natural number that needs to be multiplied with 5808 to get a perfect square number.
According to the question, $ 5808 \times y $ should be a perfect square number such that ‘y’ is the smallest natural number. To determine the value of ‘y’, we will go through all the options given and check whether the resulting number is a perfect square or not.
The smallest natural number is 1, so when 1 is multiplied with 5808 it will result in 5808 itself which is obviously not the perfect square. So, 1 is not our answer.
When we multiply 2 with 5808, it will result in 11616 which is not a perfect square. So, 2 is not our answer.
When we multiply 3 with 5808, it will result in 17424 which is a perfect square of 132. So, the correct answer is 3.
When we multiply 11 with 5808, it will result in 63888 which is not a perfect square. So, 11 is not our answer.
Hence, we can say that the smallest natural number which is multiplied by 5808 to get a perfect square number.

So, the correct answer is “Option C”.

Note: When a number is multiplied by itself then, it is the square of the number. Mathematically, $ x \times x = {x^2} $ is the square of any real number ‘x’. In other words, the product of ‘x’ and ‘x’ results in the perfect squared number.