Question

Find the smallest number by which 1100 must be multiplied so that the product
becomes a perfect square. Also, find the square root of the perfect square so
obtained.
By what smallest number must 180 be multiplied so that it becomes a perfect
square? Also, find the square root of the number so obtained.​

Answer 1

Answer:

1100, 30.

Step-by-step explanation:

1100 = 11 * 5 * 2.

Here, every prime factor appears only once. Hence to make it a perfect square, it must be multiplied by 1100 (11 * 5 * 2) itself. It gives the square root as 1100.

180 = 3 * 3 * 2 * 2 * 5.

Here, the only prime factor that doesn't form a pair is 5. hence, 180 must be multiplied by 5 to make it a perfect square. The square root thus obtained would be 3 * 2 * 5 = 30.