Question

smallest number by which 1100 must be multiplied so that the product become a perfect square. also find the square root of the perfect square so obtained

Answer 1

Prime factorization of 1100:

1100 = 2 x 550
        = 2 x 2 x 275
        = 2 x 2 x 5 x 55
        = 2 x 2 x 5 x 5 x 11

It can be written as 1100 = 2² x 5² x 11

In order to make it a perfect square, 1100 should be multiplied by 11

1100x11 = 2² x 5² x 11 x 11 = 2² x 5² x 11² = 12100.

So the perfect square obtained by multiplying 1100 by 11 is 12100.

The square root of obtained perfect square = √12100 = 110

Answer 2

Bonjour!

According to the question,

We have to find the smallest number by which 1100 should be multiplied so that the product is a perfect square.
For that we will first do prime factorisation of 1100.

1100 = 2² × 5² × 11

So, by this we can see that if we multiple 1100 by 11 we will get perfect square.

So,

1100 × 11 = 12100 (2² × 5² × 11²)

If we do square root of 12100 we will get a perfect square as,

√12100 = 110

$\sqrt{12100} = \sqrt{ {2}^{2} \times {5}^{2} \times {11}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 5 \times 11 = 110$

Hope this helps...:)