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:

110

Step-by-step explanation:

By prime factorization method

1100 = 2x2x5x5x11

To be a perfect square, its prime factor should be in pairs.

Hence the smallest number is 11, which we should multiply to get perfect square .

Square root of this perfect square number = 2x5x11 = 110.

Answer 2

ANSWERS≻

✩The smallest Number by which 1100 must be multiplied so that the product is becomes a perfect square = 11 .

$\red\bigstar$The perfect square so obtained by multiplying 1100 and 11 = 12100 .

$\blue\bigstar$The Square root of the perfect square so obtained = 110.

✳SOLUTION✳

To find out the smallest number by which 1100 must be multiplied so that the product becomes a perfect square , firstly we must do the factorization of 1100.

1100 = 2 x 2 x 5 x 5 x 11

Here all the factors of the number 1100 except 11 have pairs , so 1100 must be divided by the number 11 to make it a perfect square number .

We are also asked to find the square root of the perfect square so obtained​ , so for that we must multiply 1100 by 11

$\implies$

1100 × 11 = 12100

So , the perfect square obtained = 12100

Now , we must find the square root of 12100

$\sf \sqrt{12100} = 110$