Question

find the smallest natural number of 3042 by which it should be multiplied so as to get a perfect square also find the square root of the square number

Answer 1

it should be multiplied with 2 and its √ is 78

Answer 2

let's find the prime factorization of the given number 3042

→ 3042 = 2 x 3 x 3 x 13 x 13

$= {2}^{1} \times {3}^{2} \times {13}^{2}$

therefore, 2 is required number which should be multiplied to 3042 to make it a perfect square.

now,

$3042 \times 2 \\ \\ = 6084 \\ \\ = \sqrt{6084 } = {2}^{2} \times {3}^{2} \times {13}^{2} \\ \\ = 2 \times 3 \times 13 = 78$

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