Question

Find smallest no by which 27783 must be multipled so that it becomes a perfect square

Answer 1

27783=3×3×3×3×7×7×7
7 is left out so,we will multiply 27783 by 7 so,
27783×7=194481

Answer 2

Prime factors of 27783 = 7×7×7×3×3×3×3

Here 7 has no pair

So, 7 is the smallest number by which 27783 should be multiplied to get a perfect square.

Then,
27783×7 = 7² × 7 × 7 × 3² × 3²

= 7² × 7² × 3² × 3²

= 194481 = (441)²

Hence, the smallest number is 7 by which 27783 should be multiplied to get a perfect square.

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