Question

by what is smallest number should 15084 ×
so that product may be a perfect square​

Answer 1

Step-by-step explanation:

10584 = 2^2 × 3^2 × 7^2

now for the above to be a perfect square we can see taht we need to multiply 2×3=6 that is the least number to be multiplied to 10584 to make it a perfect square is 6

that is 10584 × 6 = 2^2 × 2^3 ×7^2 × 2 ×3 = 2^4 × 3^4 × 7^2

The square root of this number is √2^4 × 3^4 × 7^2

= 2^2 × 3^2 × 7

= 4 × 9 × 7

= 63 × 4

= 192