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.

45 points​

Answer 1

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.

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Answer 2

Step-by-step explanation:

We find 1100 = 2 × 2 × 5 × 5 × 11 =22 × 52 × 11 ∴ The prime factor 11 has no pair. ∴ If we multiply 1100 by 11, then the product becomes a perfect square. ∴ New number = 1100 × 11 = 12100

12100 = 22 × 52 × 112 √12100 = 2 × 5 × 11 = 110 Square root of the new number = 110R