For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:
Step 1: Find prime factors of the given number
By the method of prime factorization, the factors of can be determined as follows,
So,
Here, it can be observed that the prime factors and form a pair, while does not form a pair.
Step 2: Determine the perfect square number and its square root
Since could not form a pair.
Therefore, a perfect square number can be obtained by multiplying by .
So, the perfect square number
Now, the square root of the above perfect square number is,
Hence, the smallest whole number by which should be multiplied to get a perfect square is and the required perfect square number and its square root are and respectively.