Question

Find the smallest number by which 1890
must be multiplied so that the product
becomes perfect square.​

Answer 1

Step-by-step explanation:

1890 = 2 × 3 × 3 × 3 × 5 × 7

We can see that pair of 2 , 3 , 5 and 7 is incomplete . 2 × 3 × 5 × 7 is the smallest number which make it a perfect square on multiply.

1890 × 2 × 3 × 5 × 7 = 396900

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Answer 2

Answer: 210

Step-by-step explanation:

Perfect squares have factors that come in pairs. For example, 36 is the square of 6 but it can be further broken down into 2 x 2 x 3 x 3. As long as each factor has a pair, then the product will be a perfect square.

1890 has the factors 2, 3, 3, 3, 5, 7. There is already a pair of 3s. The factors still missing pairs are 2, 3, 5 and 7. 2 x 3 x 5 x 7 = 210.

If you multiply 1890 with 210, the product will be a perfect square.