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