Question

The least positive integer whose product with 9408 gives a perfect square

Answer 1

Answer:

56

Step-by-step explanation:

Since, we want to find the smallest number by which 9408 must be divided so that the quotient is a perfect square, we have to find the prime factors of 9408.

9408 = 2*2*2*2*2*2*3*7*7

Prime factors of 9408 are 2, 2, 2, 2, 2, 2. 3, 7, 7

Out of the prime factors of 9408, only 3 is without pair.

So, 3 is the number by which 9408 must be divided to make the quotient a perfect square.

9408/3 = 3136

√3136 = 56

Hence, the least positive integer is 56.

Answer 2

Answer:

3 is the least positive integer whose product with 9408 gives a perfect square

Step-by-step explanation:

Prime factorization of 9408,

9408 can be written as,

9408 = 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 3

9408  = 2² x 2² x 2² x 7² x 3

From the above we get, we have to multiply 3 to 9408 so as to get the perfect square.

Therefore the answer is 3

To find 9408 x 3

9408 x 3 = 28224

To find the square root of 28224

√28224 = 168