Question

find the smallest number by which 27783 must be multiplied so that it becomes a perfect square . solve by division method.

Answer 1

Heya dear user !!!

Here is your answer,

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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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Hope it helps.

Answer 2

Answer = 7

Step-by-step explanation:

1. Find the prime factorization which is =

3×3×3×3×7×7×7

2. Try making pairs .

We find the pairs as:(3×3)×(3×3)×(7×7)×7

3.We see that 7 is left alone and thus, 27783 must be divided by 7 so that the new no.(3969) is a perfect square .

Hope it helped !!!