Question

Which smallest whole number is to be multiplied to 2028 to get a perfect square number?
A.4
B.3
C.2
D.6

Answer 1

Hint: First, we will multiply 2028 with the smallest given number to get a perfect square. When we will multiply 2028 with 2, we will get a number which will be either a perfect square or not a perfect square. If the number is a perfect square then 2 is the smallest whole number. But if the number is not a perfect square, then we will repeat the same process by multiplying with 3, 4 and 6.

Complete step-by-step answer:
The given number is 2028. And we have to find the smallest whole number that when multiplied by 2028 gives
A whole number is any non-negative integer, which includes 0.
0,1,2, 3, … are whole numbers.
When we multiply 2028 with 2, we get 4056
 \[ \Rightarrow 2028 \times 2 = 4056\]
But 4056 is not a perfect square.
Now we multiply 2028 with 3, we get 6084
 \[ \Rightarrow 2028 \times 3 = 6084\]
And 6084 is a perfect square.
6084 is a perfect square of 78
i.e. \[{(78)^2} = 6084\]
The smallest whole number to be multiplied to 2028 to get a perfect square is 3.

Note: A whole number is any non-negative integer, which includes 0.
Which means 0,1,2, 3, … are whole numbers.
Another approach to solve this problem is:
 First, we will factorize 2028
And on factorization, we get
 \[ \Rightarrow 2028 = 2 \times 2 \times 3 \times 13 \times 13\]
The factors 2 and 13 has square but 3 does not have square,
So, we will multiply by 3 to get a perfect square number.