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.​

Answer 1

Answer:

Step-by-step explanation:

Let the number be $1100\times A$

Now,

$1100\times A = 11\times A\times (10)^2 = (\sqrt{11\times A}\times 10)^2$

In order to make the product a perfect square, we need to find the smallest A so that the product (11 x A) becomes a perfect square

Clearly, the smallest number A for which the product (11 x A) is a perfect square is 11

So, the required number is 11 and the required square root is 110