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:

First of all we will do prime factorisation of 1100.

1100=2*2*5*5*11 (*= sign of multiplication)

We observe that prime factor 11 does not form a pair.

Therefore, we must multiply the number by 11 so that the product becomes a perfect square.

;1100*11=12100

12100=(2*2)*(5*5)*(11*11)

Now, each prime factor occurs in pairs. Therefore, the required smallest number is 11.

; square root of 12100= 2*5*11 = 110

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