The least number that should be multiplied with 1008 to make it a perfect square is

The correct answer is: 7

GIVEN-
given number = 1008
TO FIND-
Number that should be multiplied with 1008 to make it a perfect square.
SOLUTION-
We know that it can be written as
1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7
Here, after pairing the same prime factors, one factor, 7, is left.
Now, multiplying 1008 by 7
We get a perfect square
Therefore, the required smallest number is 7.
FINAL ANSWER-
Option 'c' i.e. '7' is the correct answer to the given question.

Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
FINAL ANSWER REMAINS THE SAME.