Question

Find the smallest number by which 7776 is to be multiplied to get a perfect square.

Answer 1

Hint: In this problem, first we need to Find the prime factorize of the given number. Next, form the pair of the prime factors. Then, find the product of the unpaired number which is being multiplied in the given number to get a perfect square.

Complete step-by-step answer:
 In this problem, first we need to Find the prime factorize of the given number. Next, form the pair of the prime factors. Then, find the product of the unpaired number which is being multiplied in the given number to get a perfect square.
The prime factorization of the number 7776 is shown below.

Therefore,
\[7776 = \overline {2 \times 2} \times \overline {2 \times 2} \times 2 \times \overline {3 \times 3} \times \overline {3 \times 3} \times 3\]
From the above factorization, we can observe that both 2 and 3 are not in pair, hence to make the number 7776 perfect square we need to multiply it by product of 2 and 3 that is 6.
Thus, the number 7776 is multiplied by 6 to get a perfect square.

Note: To find the square root of a given number, first find the prime factorization of the given number. Then make the pair of the similar factors such that both the factors in the pair are the same. Next find the product of one factor from each pair number to calculate the square root.